4 Evaluating empirical fit
In this section, we compare the moment statistics of the model's estimates for the measurement variables to those from an unrestricted VAR of all the measurement variables. The order of the unrestricted VAR is chosen to be 4 in this experiment. The main purpose of this exercise is to evaluate how well the model fits the data. We chose only standard deviations and autocorrelation functions in the comparison.
In this exercise, we first simulate SMM for 2000 times using the Monte Carlo approach to generate 2000 data sets with each of these data sets containing the same number of observations as the historical data set.
The second step of the exercise is to generate another 2000 data set by bootstrapping the unrestricted VAR(4). We then compare summary statistics from these two large simulated data sets.
The volatility of fluctuations is usually measured using the standard deviation. In Figure 1, we check how well the model mimics the volatility of the data.
- Figure 1 - The probability density function of standard deviations
In general, the model exhibits a larger degree of volatility than those implied by the benchmark VAR. This excessive volatility suggests that we could develop the model further to improve its fit in the future.
Figure 2 shows the autocorrelation of order 1, which indicates the degree of persistence in the data. The model shows a consistent pattern of persistence as suggested by the VAR.
However, when we extend the comparison to a higher order autocorrelation (these moments are not presented in this paper), only core inflation, inflation deviations from its expectation and unemployment rate match those suggested by the data.
- Figure 2 - The probability density function of the first order autocorrelation coefficients
