# Standard Stochastic Volatility Models VS Moving Average Stochastic Volatility Model

Hi... I am comparing the log-volatility of two SV models with an application to MATLAB. Since I am a rookie in this field, I do not know if I am wrong in interpreting the graph. In my opinion the only thing I can say is that the standard SV model underestimate the volatility in the volatility is small but I am not sure of my graph. Have you ever seen something like that? Am I completely wrong?

Here the references for the models: for the SV-MA model see: Chan, J.C.C. (2013). Moving Average Stochastic Volatility Models with Application to Inflation Forecast, Journal of Econometric, 176 (2), 162-172.

and for the standard model see: Chan, J.C.C. and Hsiao, C.Y.L (2014). Estimation of Stochastic Volatility Models with Heavy Tails and Serial Dependence. In: I. Jeliazkov and X.S. Yang (Eds.),Bayesian Inference in the Social Sciences, 159-180, John Wiley & Sons, New York.

• Based on this picture, I would guess that one of the two residuals will not be distributed as $(0,1)$. Can you check the distributions of the error terms in the two models? – Kiwiakos Jun 12 '16 at 8:57
• I didn't wrote the code but maybe I can find the way to compute the residuals. However the error term of the volatility equation is normally distributed with zero mean but the variance has to be estimated...is not 1. – user22108 Jun 14 '16 at 7:32

Finally I have found the answer on my own. The problem was related to the trasformation of the dataset. The original code used: ${{y}_{t}}=400*(\log ({{P}_{t}})-\log ({{P}_{t-1}}))$ as dataset. Initially I did not care about multipling by 400 because I thought it was usless. Instead it makes a big difference. Now the two series are completely overlapped, I think it depends on how MATLAB manages the figures in the spreadsheet.