Forecasting Government Bond Yields in Thailand: A Bayesian VAR Approach

Abstract

This paper seeks to investigate major macroeconomic factors and bond yield interactions in Thai bond markets, with the goal of forecasting future bond yields. This study examines the best predictive yields for future bond yields at different maturities of 1-, 3-, 5-, 7-, and 10-years using time series data of economic indicators covering the period from 1998 to 2020. The empirical findings support the hypothesis that macroeconomic factors influence bond yield fluctuations. In terms of forecasting future bond yields, static predictions reveal that in most cases, the BVAR model offers the best predictivity of bond rates at various maturities. Furthermore, the BVAR model has the best performance in dynamic rolling-window, forecasting bond yields with various maturities for 2-, 4-, and 8-quarters. The findings of this study imply that the BVAR model forecasts future yields more accurately and consistently than other competitive models. Our research could help policymakers and investors predict bond yield changes, which could be important in macroeconomic policy development.

1. Introduction

Bond yield is one of the most important market indicators in the financial market. A yield curve is the return of a bond issued by the government at different maturities. The bond yield becomes the minimum requirement for return or a single price for using a measure of the benchmark in the debt market for governments, financial institutions, and individual investors. Although a bond’s rate of return is unaffected by uncertainty because it is known at the time of issuance, changes in the yield curve will have a direct impact on the fixed income market and other markets. Furthermore, they have a direct impact on the government’s borrowing costs for infrastructure projects and portfolio debt refinancing. Fluctuations in nominal bond yield movements cause government borrowing cost concerns and have an impact on public debt management, particularly in government debt refinancing and risk management in portfolio benchmarks.

However, as with other high-frequency financial economic data, bond yield changes are difficult to explain. Despite its expanding importance, the impact of economic factors on yield changes is still primarily determined by event-specific analysis and observations. Thai government bond yields have demonstrated a high degree of variability in recent years due to both internal and international causes, making forecasting future yields challenging. As a result, producing precise yields with various maturity estimates is critical.

Market participants have all attempted to construct good models for forecasting the yield curve. Based on different studies, there is an apparent large gap between the yield models proposed by macroeconomists, which focus on the role of economic factors in the determinants of the yields, and the models provided by financial analysts, which avoid any explicit role for such determination (Diebold et al., 2006). Several recent research studies, e.g., Diebold and Li (2006), Vicente and Tabak (2008), and Almeida et al. (2017), have investigated the forecasting accuracy of yields by using various models and comparing the forecasting performance of traditional models and linear models for the US term structure of interest rates and other yields.

However, in the existing literature, there is still very little research to forecast future yields with maturity by using a new model for emerging markets. Most emerging countries have large debt and stock markets and receive vast inflows of foreign capital, playing an essential role in the international capital market. Thailand receives attention as it has a large debt market with liquid derivative markets and thus represents an interesting investment opportunity for both domestic and external investors. In addition, all the forecasting models proposed so far in the economic and financial literature have a hard time producing forecasts more accurate than a simple no-change forecast. Recently, there has been an increasing interest in applying a Bayesian vector autoregression (BVAR) model proposed by Carriero et al. (2012) to examine a new approach to forecasting the term structure of government bond yields. In this regard, our study is more closely related to Carriero et al. (2012), who explicitly incorporate macroeconomic factors as determinants into multi-factor yield models for forecasting maturity yields.

Hence, to fill this knowledge gap in this research field, we provide the Single Equation, Vector Autoregression (VAR), and BVAR approaches to comprehensively examine macroeconomic factors that drive bond yield movements and forecast future yields with different maturities. In this paper, we aim to investigate key macroeconomic factors and bond yield interactions in Thai bond markets and compare the empirical forecasting performance of the proposed competitive linear models by fixing an in-sample and out-of-sample forecast horizon.

The paper is structured as follows. Section 2 reviews several papers relating to forecasting bond yields. Section 3 describes the data utilized for forecasting and proposes our BVAR approaches compared to other models. Section 4 presents the main results, briefly discusses the model estimation and forecast, and presents a comparison of the forecasting performance estimated by each model. Finally, Section 5 provides conclusions and some policy recommendations.

2. Literature Review

In the past two decades, many researchers have been interested in forecasting future bond yield movements with macroeconomic factors such as GDP growth, inflation, debt-to-GDP, short-term interest rate, stock market index, and exchange rate. A number of empirical studies on the determinants of government bond yields with different maturities have demonstrated the power of domestic and global macroeconomic factors in explaining yield movements. Many researchers employ event study methodology to explain the relationship between macroeconomic variables and bond yield movements in the bond markets (Ludvigson & Ng, 2009; Megananda et al., 2021; Trinh et al., 2020). These researchers study the economic factors that have the power to drive maturity yield movements. The results of their studies indicate that macroeconomic fundamentals such as debt-to-GDP ratio, fiscal deficit, fed rate, public debt, return of the stock market, current account deficit, interest rate, exchange rate, unemployment, and inflation, are more significant as determinants of government bond yields.

Furthermore, Diebold et al. (2005) apply a simple nonstructural VAR to examine the nature of linkages between the macro-finance factors driving the bond yield curve and macroeconomic fundamentals. The results of their study suggest that there is strong evidence of the impacts of macroeconomic factors on future movements in the bond yield curve and evidence of a reverse influence as well. Additionally, Perović (2015) applied a static panel model to analyze the magnitudes of the effects of government debt and primary balance on long-term government bond yields in 10 Central and Eastern European countries from 2000 to 2013. The results of this study show that a one percentage point increase in the stock of government debt is correlated with an increase in government bond yields of 2.7–4 basis points, while a one percentage point increase in the primary deficit to GDP ratio is associated with an increase in government bond yields of 12.9–24.3 basis points.

Also, Dai Hung (2020) used a time-varying structural vector autorepression (TVC-VAR) approach to investigate the impacts of macroeconomic variables on bond yield curves. These results are in line with other empirical studies that suggest that macroeconomic fundamentals also drive the government bond yield curves. Similarly, Anwar and Suhendra (2020) used traditional panel VAR to examine the effect of monetary policy independence shocks on bond yields. The findings of this study showed that monetary policy shocks have an effect on bond yields, 6 periods after they occur.

Cebula (1997) used cointegration analytic methodologies to examine the impact of net capital inflows on domestic interest rate variables, according to the empirical literature review on global macroeconomic determinants. The findings suggested that the influence of net international capital inflows on domestic interest rates in France may not only lower long term rates but also offset a significant portion of the long term yield impact of the country’s government budget deficit. This is most likely attributable to global variables such as international capital inflows, which have become one of the most important drivers of domestic bond yields.

In the case of forecasting future bond yields with different maturities, most of the literature studies apply various economic models to forecast the bond yields both in-sample and out-of-sample. Most of the existing evidence focuses on statistical measures of forecast accuracy with the models. Several papers have evaluated the forecast performance of the models by looking at statistical measures (Giacomini & Rossi, 2010). Carriero et al. (2012) introduced a new statistical model for the entire term structure of interest rates (U.S. Treasury dataset using a rolling estimation window of 120 months, from 1985 to 2003) and compare the forecasting performance of the proposed model to most of the existing alternative specifications.

This research uses several models for out-of-sample forecasting of U.S. yields, such as Random Walk (RW), Univariate Autoregressive (AR), VAR, Affine Term Structure Model (ATSM), Dynamic Nelson and Siegel model, Diebold-Li model, and Bayesian VAR. The finding indicated that the proposed Bayesian VAR approach produces competitive forecasts that are systematically more accurate than RW forecasts at all maturities and forecast horizons, even though the gains are small, and it outperforms all other models. Moreover, they find that in the class of linear models, powering up produces an overall better forecast than the other models (direct approach), both for AR and VAR models.

Similarly, Almeida et al. (2017) used data from the US Treasury to estimate bond yields and then compare them to successful term structure benchmarks based on the out-of-sample forecasting performance of segmented term structure models with 8 maturity yields covering the period from 1985 to 2012.

The several models used for measuring the rolling window forecast performance with RW are the Diebold and Li (2006) model, Svenson model (DSM), polynomial segmented model, Affine Gaussian, weak segmented (NS4), and strong segmented (NS4S), all with AR factor dynamics. The finding shows that a series of out-of-sample forecasts of U.S. Treasury yields produced by the segmented models have a significantly lower RMSE than those produced by the RW and some other established term structure models.

Vicente and Tabak (2008) also looked at alternative models for forecasting fixed income rates in Brazil, using four distinct interest rate swaps with varying maturities. Using mean squared errors and Diebold-Mariano statistics, they compare the accuracy of out-of-sample forecasting of the Diebold and Li (2006) model, the affine term structure model, and the RW benchmark. The empirical findings showed that the Diebold and Li (2006) model gives better forecasts than the other models, particularly for short-term yields over the long run.

Furthermore, Diebold and Li (2006) forecasted the term structure of government bond yields using the Nelson-Siegel model and a number of yield models. Using data from the US Treasury from 1985 to 2000, this study assesses the yields’ out-of-sample predicting performance. The Nelson-Siegel yield curve as a three-factor dynamic model (level, slope, and curvature) forecast looks to be significantly more accurate than the RW over long horizons, but the 1-month ahead forecast is no better than the RW and the other models.

However, the aforementioned empirical papers are mostly based on the traditional approaches that are used to forecast the future term structure of fixed income yields with different maturities. Most of the models are direct approaches estimated by using only the yields without any macroeconomic consideration. In recent research, linear models have been very popular and tend to produce better overall forecasts of economic indicators and yields than other direct approaches. Hence, based on the current literature above, we propose Bayesian VAR and linear models (i.e., VAR and Single Equation) with economic factors for forecasting bond yields with different maturities in accordance with the objectives of this study and compare their forecasting performance to that of competitive models and Random Walk forecasts.

3. Data and Methodology

3.1. Data

Given the objective of this study, we use the end of the quarter Thai bond yield data from 1998: Q1 to 2020: Q4. This yielded data is used to calculate the nominal fixed-income yields with maturities of 1-, 3-, 5-, 7-, and 10-year from the ThaiBMA. As for macroeconomic factors, we consider the primary budget deficit (PB), the fed’s policy rate (FED), the all-commodity price index (ACPI), capital inflow, the VIX index (CBOE volatility index), and liquidity (LQ), which are all obtained from the database of the Ministry of Finance, the Bank of Thailand, and the Stock Exchange of Thailand. In addition, some variables are obtained from the International Monetary Funds and the CEIC Database.

We consider these factors as they are widely recognized to be the common set of economic fundamentals required to capture macroeconomic dynamics and also include new indicators such as commodity prices, and capital inflow into this study. The six variables represent the fiscal policy instrument, the monetary policy instrument, the financial market indices, and international indicators, respectively. Most of the datasets for domestic and international factors are available at a monthly frequency, but they are converted to a quarterly basis covering the period from 1998: Q1 up to 2020: Q4.

3.2. Methodology

3.2.1. Single Equation Model

The single Equation model is used in econometrics to estimate models in which a single variable of interest is determined by one or more exogenous explanatory variables. The forecasts are then derived such as the following:

Y_t = β₀ + Σβ_1−k X_{1−k, t−i} + ɛ_t,       (1)

Where Y_t denotes the endogenous variable at time t, X_{t – i} are lag (1 to k) of (predictive) exogenous variables.

3.2.2. VAR Model

We also consider the standard VAR approach. This approach is considered an alternative to the large-scale macro-econometric models. The reduced-form VAR model is defined by the following dynamic equation:

Y_t = A(L) Y_t–1 + ε_t       (2)

Where Y_t denotes the vector of endogenous variables; L represents lag operator; A(L) is a matrix of reduced-form coefficients relating past variable values to current values; and ε_t is the vector of reduced-form errors with covariance matrix ∑_ε.

The VAR methodology, it allows for estimating the multi factors of internal and external shocks and their impacts on government bond yield movements. Moreover, it can also provide forecasts of future yields with different maturities. However, a standard VAR model has a severe limitation on estimated factors. For example, in a traditional VAR model, a strategy may encounter an overparameterization problem because the number of estimated parameters (p(k–1)) rapidly reduces the degree of freedom of the VAR system and cannot be greater than the number of large variables (Bernanke et al., 2005). The lag selection is based on the Akaike Information Criterion (AIC).

3.2.3. BVAR Model

In this paper, we followed the Bayesian VAR approach originally developed by Litterman (1986). The Bayesian VAR is built on the VAR model by applying Bayesian methods to estimate a VAR. The difference with the standard VAR approach lies in the fact that the model parameters are treated as random variables, and prior probabilities are assigned to them. The Bayesian model imposes Theil- Goldberger inaccurate restrictions on the VAR coefficients through the use of hyper-parameters, known as “Minnesota prior”, which reflects the belief that economic structures normally follow a multivariate random walk and that the econometric equations can be estimated separately.

Bayesian inference is the set of rules for transforming an initial distribution into an updated distributional condition on observations. Bayesian priors are often used to control the otherwise highly over-parametrized VAR models. The main advantage of the Bayesian VAR model is that it avoids the problems of collinearity and over-parameterization that often occur with the application of VAR model since Bayesian VAR imposes priors on the autoregression (AR) parameters and corrects coefficient bias resulting from series non-stationarity.

The BVAR method is set up by stacking the estimated bond yields at various maturities and linking them with a matrix of predetermined economic linkages. The basic idea of Bayesian estimation is to think about model coefficients in terms of conditional probabilities rather than about parameters with a fixed “true” value, which enables us to estimate large-dimension VAR using Bayesian shrinkage.

To derive the Bayesian VAR model, we begin by considering a general VAR model of a P dimensional column variable and y_t with M of the form. We can re-write the model equation as:

y_t = θ₀ + θ_m y_t–1 + θ_m y_t–2 + ... + θ_M y_t–M + ε_t       (3)

Where y_t P × 1 a vector where P is the number of variables, θ₀ is P × 1 a vector, θ_m is P × P a matrix with m = 1, ..., M, where M is the number of lags, ε_t is P × 1 vector and the errors ε₁, ..., ε_T are iid N_p (0, Σ), and Σ is p × p positive definite error covariance matrix. Let define:

\(\boldsymbol{y}_{t}=\left[\begin{array}{c} y_{1, t} \\ y_{2, t} \\ \vdots \\ y_{P, t} \end{array}\right], \boldsymbol{\theta}_{0}=\left[\begin{array}{c} \theta_{01} \\ \theta_{02} \\ \vdots \\ \theta_{0 P} \end{array}\right], \boldsymbol{\theta}_{m}=\left[\begin{array}{cccc} \theta_{11} & \theta_{12} & \cdots & \theta_{1 M} \\ \theta_{21} & \theta_{21} & \cdots & \theta_{2 M} \\ \vdots & \vdots & \ddots & \vdots \\ \theta_{P 1} & \theta_{P 2} & \cdots & \theta_{P M} \end{array}\right],\\ \boldsymbol{x}_{t}=\left[\begin{array}{cccc} y_{1, t-1} & y_{1, t-1} & \cdots & y_{1, t-M} \\ y_{2, t-1} & y_{2, t-1} & \cdots & y_{2, t-M} \\ \vdots & \vdots & \ddots & \vdots \\ y_{P, t-1} & y_{P, t-1} & \cdots & y_{P, t-M} \end{array}\right], \boldsymbol{\varepsilon}_{t}=\left[\begin{array}{c} \varepsilon_{1, t} \\ \varepsilon_{2, t} \\ \vdots \\ \varepsilon_{P, t} \end{array}\right]\\ Y=\left[\begin{array}{c} y_{1} \\ y_{2} \\ \vdots \\ y_{P} \end{array}\right], \Phi_{0}=\left[\begin{array}{c} \theta_{1} \\ \theta_{2} \\ \vdots \\ \theta_{P} \end{array}\right], X=\left[\begin{array}{llll} x_{1} & x_{2} & \cdots & x_{M} \end{array}\right], E=\left[\begin{array}{c} \varepsilon_{1} \\ \varepsilon_{2} \\ \vdots \\ \varepsilon_{P} \end{array}\right] \)

Where

\(\begin{aligned} &\theta_{1}=\left[\begin{array}{llll} \theta_{01} & \theta_{11} & \ldots & \theta_{1 M} \end{array}\right] \\ &\theta_{1}=\left[\begin{array}{llll} \theta_{02} & \theta_{21} & \ldots & \theta_{2 M} \end{array}\right] \\ &\vdots \\ &\theta_{P}=\left[\begin{array}{llll} \theta_{0 P} & \theta_{P 1} & \ldots & \theta_{P M} \end{array}\right] \end{aligned}\\ x_{1}=\left[\begin{array}{c} 1 \\ y_{1, t-1} \\ \vdots \\ y_{P, t-1} \end{array}\right], x_{2}=\left[\begin{array}{c} 1 \\ y_{1, t-2} \\ \vdots \\ y_{P, t-2} \end{array}\right], \ldots, x_{M}=\left[\begin{array}{c} 1 \\ y_{1, t-M} \\ \vdots \\ y_{P, t-M} \end{array}\right]\)

Thus, we have

Y = XΦ + E       (4)

Now, we will discuss based on Bayes’ Theorem. Let P(θ) is the probability of θ, P(θ/Y) is the conditional probability, and P(Y) is the marginal probability. The joint probability of obtaining such θ data Y is defined by P(θ ∩ Y) = P(θ/Y) P(Y) and vice versa. Hence, we get

\(P(\theta / Y)=\frac{P(Y / \theta) P(\theta)}{P(Y)}\)       (5)

P(θ) and P(θ/Y) are, respectively, the prior and posterior distribution of θ, given the observed data Y. In the parameter space, we have P(Y) = ∫P(Y/θ)P(θ)dθ which is a constant that normalizes the kernel of the posterior distribution. Thus, we can rewrite (5) as follows:

P(θ/Y) ∝ L(θ;Y)P(θ)       (6)

Where L(θ;Y) denotes the likelihood function.

Thus, the solution to the Bayesian VAR model is obtained. The general model equation will take the form as:

\(Y_{t}=\theta_{0}+\sum_{i=1}^{k} \theta_{m}\left(X_{i}\right)+\varepsilon_{t}\)       (7)

Then, we focus on evaluating the forecasting performance of the models by looking at the statistical measures (i.e., Root Mean Squared Error and Theil’s Inequality Coefficient) and discussing the procedures used in the derivation of the forecasts (Carriero et al., 2012). We also compare these models based on multiple forecasting exercises by considering the accuracy forecast error measure with the Random Walk to investigate the best performance of forecasting yields with maturity accuracy. Given our goal, we adopt both static and dynamic forecasting with recursive and rolling-window methods for the 104 in-sample and out-of-sample forecasting performed.

4. Empirical Results and Discussion

In this paper, we present and discuss the empirical results based on forecasting government bond yields at various maturities by fixing an in-sample and out-of-sample window size equal to 104 quarterly data by estimating static and dynamic forecasts in the Single Equation, VAR, and Bayesian VAR approaches. We use the Random Walk forecasts as the benchmark with respect to comparing the forecasts of all the competing models.

4.1. Unit Root Tests

To analyze the integration properties of the individual series, we adopt the Augmented Dickey-Fuller (ADF) test. Concerning the results of the unit root test based on the ADF approach, we can conclude that the data stationary condition is satisfied. Overall, the results of the unit root test show that all the series do not have a unit root and are stationary at the first order, namely I(1).

4.2. Yield and Economic Factor Estimation

To analyze the effect of economic factors on the bond yields with maturities of 1-, 3-, 5-, 7-, and 10-year, the data sets are investigated by using the SE, VAR, and BVAR methods to examine the association between macroeconomic variables and government bond yields in the Thai bond market. This study obtains the six key variables, namely the fed rate, primary budget deficit, commodity price index, capital inflow, VIX index, and liquidity. These variables are widely considered to be the fundamentals needed to capture basic macroeconomic dynamics.

In Table 1, the results display the estimates of the parameters of the crucial macro factors and government bond yield interactions. Overall, the parameter estimates are significant, with a small associated standard deviation. The results of the VAR estimate show that the coefficient of each macroeconomic variable appears significant effects on bond yields with different maturities, but the adjustments of R-square and F-statistic are quite low. Also, the results of the Single Equation estimate are likely to be the same as the VAR’s results. In contrast, compared with the Bayesian VAR estimate, the results show that in most cases, the coefficients of macro variables have a significant effect on the bond yield movements at various maturities, with very high adjustments of R-square and F-statistic of up to 0.8 and 25, respectively. This means that the BVAR approach is suitable to estimate the best predictability more accurately than another one. Furthermore, we find that new economic variables added in this area (commodity price index and capital inflow) have a significant effect on the yields at various maturities.

Table 1: VAR Model, BVAR Model, and Single Equation Parameter Estimate

Note: ***, ** and * indicate 1%, 5%, and 10% levels of significance based on t-statistics.

4.3. Static Forecasting Performances of Yields

To assess the forecasting performance of the Single Equation, VAR, BVAR, as well as RW forecasts are used as the benchmark by looking at statistical measures. In this paper, we provide a measure of yield forecasting performance. In particular, we employ five core statistical functions to measure four usual approaches, including MAE, MAPE, MSE, RMSE, and Theil (Giacomini and Rossi (2010) develop statistical tests). Then, using a static forecast technique in all models, we look at forecasting government bond yields at various maturities by fixing an in-sample of 24 data. The prediction is done for 2020:Q4, with an in sample period from 2015:Q1 to 2020:Q4. The empirical forecasting results are presented.

We present comparisons of four models as mentioned above. The results show the forecasting performance of bond yields with different maturities of all the models. Overall, the results in terms of the measure of the forecasting performances of all models are displayed in Table 2. The results show that the BVAR model has the best performance in forecasting bond yields with various maturities, with the exception of the 10-year maturity, where the RW forecast outperforms the BVAR model. Most figures of the BVAR model of these statistical functions measured are the lowest, and the RMSE and Theil of the evaluations of all yields (short-term, medium-term, and long-term yields) are smaller than one signal, indicating that the model under consideration strongly outperforms the SE, VAR, and RW models, but the figures of the RW forecast (10-year maturity yield) beat all the models. However, overall, these model forecasts are generally more accurate than those of most of the competitive models in a robust way. For instance, the average RMSE and Theil of the BVAR method when forecasting short-term yield maturity (1-year yield) with an in-sample of 24 quarters are very low and equal to 0.1627 and 0.0543, respectively. For the poor performance of other models in the table, compared with the same yields, the values of the SE model’s evaluations are high and equal to 0.1818 and 0.0604. The values of the RW’s evaluations are also high and equal to 0.1888 and 0.0552. Similarly, an entry with the VAR model’s evaluations has higher RMSE and Theil values than other models, and the values are equal to 0.1902 and 0.0627, respectively.

Table 2: Comparison with VAR, Bayesian VAR, Single Equation, and Random Walk Static Forecast Evaluation (2015–2020)

Note: In-Sample 24 observations from 2015q1 to 2020q4. BVAR model evaluations have the best predictability due to the smallest values, except for the 10-year maturity, where the RW forecast beats the BVAR model.

4.3.1. Static Forecasting Error for the Short-Term Yields

Given the 1-year yield, we consider the forecast error measure to investigate the best performance of the forecasting yield. The results show that all models have impressive performances, especially the BVAR model, which gives fewer forecast errors in the whole period when compared with the actual short-term yield for all forecasting horizons. This is illustrated by the static forecast of a 1-year yield with competitive models plotted in Figure 1. As for the case of the VAR model, the magnitude of forecast errors from the actual 1-year maturity is a maximum increase of 0.42% and a minimum increase of 0.01%. Explicitly, the percentage of forecast errors of the BVAR model has a small and significant effect on the actual bond yield, with a maximum increase of 0.40% and a minimum increase of 0.01%. In terms of the SE model, the percentage of forecast errors (0.41%) is relatively small compared to that of the VAR method, but its minimum error is likely to be higher than the BVAR model. For the RW forecast, the percentage of forecast errors (0.38%) is relatively small compared to that of the VAR, BVAR, and SE models, but its minimum error (0.02%) is higher than all other models.

Figure 1: Static Forecast Error of Short-Medium-Long-Term Yields

4.3.2. Static Forecasting Error for the Medium-Term Yields

In the case of medium-term yields, our evidence shows that the forecast errors of all models have fluctuated from most of the actual yields with 3- and 5-year maturities (see Figure 1). Regarding the percentage of forecast errors for the 3-year yield, all models provide the evident errors from the actual yield with a maximum increase of 0.47% (VAR), 0.50% (BVAR), 0.50% (SE), and 0.37% (RW). In other words, these models have small errors of 0.02% (VAR), 0.00% (BVAR), 0.01% (SE), and 0.01% (RW). Considering the forecast errors for the 5-year yield, the magnitude of forecast errors of all models is a maximum increase of 0.63% (VAR), 0.47% (BVAR), 0.57% (SE), and 0.53% (RW), respectively. For small forecast errors of each model, both BVAR and RW have a value error of 0.001%, whereas to VAR and SE models have large errors of 0.03% and 0.015%, respectively.

4.3.3. Static Forecasting Error for the Long-Term Yields

In the case of long-term yields, the results show that all models generate the forecast errors from the actual bond yields at different values (see Figure 1). In terms of the 7-year yield, unlike other cases, VAR’s forecast error is smaller than that of other models, with a maximum increase of 0.74%, but the error values of the BVAR, SE, and RW models are at a high level of 0.80%, 0.75%, and 0.80%, respectively. However, the minimum of RW’s forecast error is less than the others at 0.00%, while the minimum forecast errors of the VAR, BVAR, and SE models are equal to 0.02%, 0.03%, and 0.07%, respectively. In the case of the forecast errors for the 10-year yield, the magnitude errors of all models cause a change from the actual yield with a maximum increase of 0.68% (VAR), 0.68% (BVAR), 0.75% (SE), and 0.68% (RW), respectively. For lower forecast errors of each model, the BVAR and SE models have small errors of 0.004%, compared to RW and VAR’s errors of 0.009% and 0.02%, respectively.

4.4. Dynamic Rolling Forecasting Performances of Yields

For computing our results, we use a dynamic rolling window forecasting evaluation of 104 quarters (22 years) with only the VAR and BVAR models. In this study, we produce forecasts for all the horizons up to 3 rolling windows ahead by presenting results for the 2-, 4-, and 8-quarter rolling ahead. The initial estimation window is from 1998:Q1 to 2016:Q3, and the initial forecast windows, are for 2-quarter rolling (2016:Q4–2017:Q1), 4-quarter rolling (2016:Q4–2017:Q3), and 8-quarter rolling (2016:Q4– 2018:Q3). We then compute a rolling scheme, repeating this procedure until the last forecast window with out-of-sample 17 quarters. The empirical forecasting results are finally presented.

The results show the forecast performance of bond yields with different maturities across all models. Overall, the results in terms of the measure of the dynamic rolling forecast performances of two models are displayed in Table 3. The results indicate that the BVAR model has the best performance in dynamic rolling-window forecasting bond yields with various maturities of 2-, 4-, and 8-quarter rolling ahead. The statistical evaluations show that most figures of the BVAR model with all rolling forecasts are the lowest and outperform the VAR model at all maturities. Explicitly, all RMSE and Theil values of the BVAR’s rolling forecast of all yields (short-term, medium-term, and long-term yields) are lower than one, which means that the BVAR model is better than the VAR model. Still, it is very interesting to note that the BVAR model with all rolling forecasts is generally more accurate than another competitive model in a robust way. For example, in the case of the 5-year yield, all RMSE and Theil values of the BVAR method with 2-, 4-, and 8-quarter rolling forecasts are lower than one (RMSE = 0.2695, 0.1369, and 0.0340) and (Theil = 0.0086, 0.0044, and 0.0002). Meanwhile, the competitive model (VAR), considering the same yield with rolling forecast evaluations, produces higher values of RMSE (0.3502, 0.4692, and 0.0413) and Theil (0.0110, 0.0145, and 0.0007).

Table 3: Comparison with VAR Model and Bayesian VAR Model Dynamic Rolling Forecast Evaluation (2016–2020)

Note: Out-of-Sample 17 observations from 2016q4 to 2020q4. Dynamic rolling forecast evaluations are Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), and Theil Inequality Coefficient (Theil). BVAR’s dynamic rolling forecast evaluations have the best predictability as all values are the smallest.

4.4.1. Dynamic Rolling Forecast Error for the Short-Term Yields

For the 1-year yield, we find that, overall, the BVAR model with all rolling forecasts works better than the VAR model plotted in Figure 2. The BVAR model produces very good forecasts in all periods in which the percentage of forecast errors from the actual yield is lower than another model with a maximum-minimum value of 2-quarter (0.72%, 0.01%), 4-quarter (0.87%, 0.01%), and 8-quarter (0.69%, 0.005%). As for the VAR model, the rolling forecast errors from the actual yield are high, with a maximum-minimum value of 2-quarter (0.74%, 0.04%), 4-quarter (0.83%, 0.04%), and 8-quarter (0.85%, 0.11%).

Figure 2: Dynamic Rolling Forecast of Short-Medium-Long-Term Yields

4.4.2. Dynamic Rolling Forecast Error for the Medium-Term Yields

In terms of the medium-term yields, our evidence shows that most of the BVAR’s rolling forecasts are better than those of the competing model, except in some cases where the magnitude errors of the VAR model (2- and 4-quarter rolling forecasts) are lower a plotted in Figure 2. The results show that the magnitude errors for the 3-year yield are less than the actual yield in the VAR’s rolling forecast by a maximum increase of 0.64% (2-quarter), 0.78% (4-quarter), and 0.85% (8-quarter), respectively. The BVAR model generates higher errors only in a few cases, such as rolling forecasts of 2- and 4-quarters ahead by an increase of 0.70%, 0.80%, and 0.67%, respectively. However, the magnitude of the minimum forecast error of the BVAR model has very little value. Its forecast error from the actual yield is lower in all cases by an increase of 0.01%.

For the 5-year yield, we find that the magnitude errors of the BVAR model are lower than those of the VAR, except in the case of 2-quarter rolling. When comparing their forecast errors, both models have a maximum increase of 2-quarter (0.67%, 0.63%), 4-quarter (0.76%, 1.0%), and 8-quarter (0.63%, 0.81%), respectively. For small forecast errors of each model, the BVAR model has low errors of 0.07%, 0.04%, and 0.04%, compared to the VAR model which has errors of 0.05% in all cases.

4.4.3. Dynamic Rolling Forecast Error for the Long-Term Yields

In the case of long-term yields, our evidence shows that BVAR’s forecast errors from the actual bond yields are better than those of the VAR, as plotted in Figure 2. For the 7-year yield, the magnitude errors of the BVAR model are smaller, except in the 2-quarter rolling forecast, where the BVAR model’s value is higher. Their forecast errors as follows: 2-quarter (0.88%, 0.75%), 4-quarter (1.11%, 1.14%), and 8-quarter (0.96%, 1.44%). The minimum of VAR’s forecast error is lower only in the 4-quarter rolling forecast by an increase of 0.0004%. For the rest, the BVAR and VAR models produce a similar error of 0.01%.

For the 10-year yield, the magnitude errors of the BVAR model cause a change from the actual yield that is lower than the VAR model, with the following maximum increases: 2-quarter (0.67%, 0.83%), 4-quarter (0.74%, 0.99%), and 8-quarter (0.61%, 1.01%). The forecast errors of the BVAR model are lower than those of the VAR model, with the following minimum increases: 2-quarter (0.01%, 0.03%), 4-quarter (0.05%, 0.03%), and 8-quarter (0.01%, 0.05%).

4.5. Forecast the Future Bond Yields in the Next 3 Years (2022f–2024f)

In terms of bond yield predictability, we find that a Bayesian VAR model is the best strategy since it delivers a more accurate forecast over longer time periods than other models. As a result, we utilize a Bayesian VAR model with a dynamic forecast technique to project future bond yield movements over the next three years for various maturities (2022f–2024f).

According to the results of BVAR’s forecast, Thai government bond yields are expected to rise by 0.32 percent on average over the next three years. In short-to-long-term yields, the yield curve tends to rise, and its shape is likely to steepen. The Fed may raise short-term interest rates, which will cause the yield curve to steepen during the following three years. An increase in the Fed’s short-term rate objective normally leads to an increase in longer-term rates, which in turn impacts yield movements in global financial markets, including the Bank of Thailand’s policy rate. Furthermore, the yield curve tends to increase in line with the Thai government’s bond supply throughout the same time period, as the government must continue to issue new bonds of different maturities to finance the annual budget deficit, support economic development, and restructure public debt.

We discovered that over the years 2022–2024, the movement of yields with various maturities (1, 3-, 5-, 7-, and 10-year) is likely to increase (see Figure 3). This reflects the high costs of a new government borrowing for funding needs, including public debt management, government debt refinancing, infrastructure projects, and portfolio risk management. Furthermore, an increase in yields may result in higher portfolio returns for investors or speculators.

Figure 3: Forecast Thai Bond Yield Curve in 2022–2024

Then we examine the risks of increasing yields for bond market participants. As previously stated, any shift in the yield curve will reflect the government’s high borrowing costs, as it is the largest issuer in the bond market. We estimate that Thailand’s funding needs will rise by an average of THB 1.6–2 trillion each year between 2022 and 2024, based on projections. The interest debt load of government borrowing will change as future predicted yields will increase. We estimate that yield swings will increase by 10 to 150 basis points every year. This might increase the interest debt burden of government borrowing by an average of 1.03 percent, 0.70 percent, and 0.88 percent between 2022 and 2024.

5. Conclusions and Policy Implications

In this paper, we look at how and why macroeconomic factors affect government bond yields in Thailand for various maturities (1, 3, 5, 7, and 10-year yields). To investigate the relationship between macroeconomic variables and government bond yields, we used the SE, VAR, and Bayesian VAR methods to specify and estimate the bond yield and macroeconomic factors (fed rate, primary budget deficit, commodity price index, capital inflow, VIX index, and liquidity).

The static forecast findings demonstrate that the BVAR model has the lowest figures of all statistical functions measured, and the RMSE and Theil of all yield evaluations are less than one, showing that the model under consideration beats the SE and VAR models significantly. RW, on the other hand, outperforms the BVAR model for long-term yield (10-year maturity). The results suggest that in-sample forecasting has a strong track record. Furthermore, we discover that the static prediction of short-term yields has a lower inaccuracy than the forecast of medium-term and long term yields for various forecasting horizons when compared to the actual yield.

The results show that the BVAR model performs the best in dynamic rolling-window forecasting of future bond rates with 2-, 4-, and 8-quarter rolling ahead maturities. Most BVAR figures with all rolling projections appear to be the lowest and outperform the VAR model at all maturities, according to statistical analyses. Explicitly, the RMSE and Theil of the BVAR’s rolling forecast of all yields (short-, medium-, and long-term yields) are all less than one, indicating that the BVAR model is superior to the VAR model. Nonetheless, it’s worth noting that the BVAR model with a rolling forecast horizon is consistently more accurate than the competitive models.

This study’s findings have resulted in a significant policy suggestion. Bond yields must be predicted while macroeconomic fluctuations are taken into account. As a result, our article suggests that governments, fixed income portfolio managers, financial regulators, financial institutions, risk managers, and others use a Bayesian VAR approach to adjust bond yields with varied maturities changes. The BVAR model anticipates bond yields more accurately over longer time periods than linear models and RW predictions.