Nonlinear Exchange Rate Dynamics in Iran using the Bayesian Nonlinear Method

Exchange rate is a measure of the equality of a country's currency against the currencies of other countries. It indicates the measurement of that country's economic situation in comparison with other countries. In the framework of conventional economic theory, the exchange rate system refers to the mechanism of determining the exchange rate through market forces exerted on the supply and demand.The purpose of this study is to understand the dynamics governing the exchange rate behavior using nonlinear models. By understanding the exchange rate dynamics, one can recognize its unusual and worrying behavior over time and apply the necessary policies accordingly.

The baseline linear model used in this study is a finite-order autoregressive (AR) model with relation (1):(1) In the real logarithm of the real exchange rate, the interrupted polynomials are placed in the roots of ϕ (z) = 0 on or outside a single circle. The roots outside the unit circle mean that PPP remains stable in the long run.Regime change regressionTwo-mode TAR (2) models are defined as follows:(2)  In the above relation, there is a sequence of white noises with mean zero and variance 1. In this model, it is assumed that the variance in each regime is different from that in the other regimes. In order to complete the above definition, the R1 and R2 regimes need to be described more precisely. It depends on how each regime changes over time.Introducing the Bayesian modelIn order to estimate the Bayesian SETAR, we assume that the exchange rate variable has a normal distribution.(3)  In the SETAR model, the regime change is defined as a discrete variable as follows:In the next step, in order to have a Bayesian estimate, we need to specify the backgrounds of the model coefficients and the other parameters. An appropriate assumption in this regard is to assume that the anterior distribution r is a continuous uniform distribution whose boundaries include the minimum and maximum time series data as follows:In the next step, we will define the backgrounds for the coefficients. According to the objectives of this study, we will use the background for the ignorance of the normal part as follows:Bayesian estimation methodThe basis of Bayesian inferences is Bayesian theorem. According to this theorem, the posterior probability of an event varies according to the product of the previous probability in the logarithm of the orthogonality. In mathematical terms, Bayes' theorem is as follows:

Table 1 reports the results of the SETAR model estimation for the exchange rate return (Rials against the dollar with the monthly rotation in the period from 2004 to December 2020). The validity intervals of the coefficients are adjusted and do not include zero, which, like the classical case, is based on the significance of these  coefficients. Table 1. Bayesian SETAR model coefficients (1) for the dollar exchange rateCoefficients Posterior average Posterior  standard deviation95% confidence interval 0,00790,0023(0,0034;0,0123) 0,31790,0713 (0,1773;0,4567) 0,01470,0161(-0,0172;0,0465)  0,43380,1468(0,1427;0,7244) 0,02230.0006 (0,0208;0,0230) Table 2. Variances of the two regimes in the Bayesian  SETAR (1) model for the dollar exchange rate Coefficients Posterior  average Posterior standard deviation95% confidence interval 0/00070/0001(0,0006;0,0009) 0/00940/0019 (0,0064;0,0137)  According to the results of Table (2), when the exchange  rate is lower than the latter value of thresholds, its variability is much less than when the  exchange rate is higher than the threshold value (variance in regime 2 is greater than that in regime 1)Figure (1) shows the autocorrelation of the simulated values in the latter estimation of the model parameters in the two regimes. Figure 1. Autocorrelation of the posterior coefficients in both regimes 1 and The results in Figure 1 show that the correlation of the simulated values for all the model parameters rapidly decreases to zero. Therefore, we are faced with a suitable sample of values to simulate the posterior distribution of the parameters. There is also no need to increase the simulation volume.Figure (2) shows the effect curves of all the later parameters of the model used in this research: Figure 2. Effect diagrams for the SETAR pattern parameters (1) Based on the findings about the curve of the effect related to all the parameters, no regular pattern exists in the simulated values ​​of the parameters. Therefore, the stability of these coefficients is confirmed, and the results of the Bayesian model SETAR (1) used in this study are statistically valid. 

The exchange rate as a price variable plays a very important role in the performance of an economy. The results of this study indicate that there are two exchange regimes in which the exchange rate adjustment parameter will be in equilibrium with a 95% probability in regime 1 (0.1773,0.4567). This is very small due to the deviation of the latter standard of this coefficient (S. Dev = 0.0713). Also, the same parameter with a 95% probability in regime 2 will be at the distance (0.1427, 0.7244), which is a relatively long distance. The results showed that this is due to the high volatility of the exchange rate in regime 2. In addition, the adjustment in the first regime to the long-term equilibrium path is much safer than the adjustment to the long-term path in the second regime because the variability in the conditions of the exchange rate increase is very high. Finally, the results of this study showed that the expansionary exchange rate regime (regime 1) has a deviation from higher regime standards than the mild exchange rate regime (regime 2), which indicates high currency fluctuations in this regime and more uncertainty. So, using regime 1 provides the conditions for a proper economic growth in the future.