# Model to test seasonality of funds

My dissertation is about funds seasonality. The model that I am using is an OLS regression with dummies to check if January has a return greater than the remaining period:

$$R_t = B_0 + B_1 D_{mt} + U_t$$

• $R_t$ is the return on funds
• $B_0$ is the intercept
• $D_{mt}$ is the dummy variable. The value 1 corresponding to January and 0 otherwise
• $U_t$ is error term

What tests do I have to run?
I am checking for heteroscedasticty (White test) and serial correlation (Durbin-Watson test).
Do I need to run other tests?

• How many months of data do you have? How many funds? – Dimitriy V. Masterov Jul 28 '16 at 4:36
• I have 132 months (eleven years). I have 148 funds... – D. Adams Jul 29 '16 at 2:16
• I was going through my old answers and noticed this one was not accepted. Do you perhaps need further clarification? – Richard Hardy Feb 20 '17 at 15:17

I would start by performing one of the tests for unit roots (or stationarity) for panel data panel datasets.

If the returns are stationary, I would fit a fixed effects linear regression model with a dummy for January. I would use heteroskedasticity-robust errors or perhaps cluster them by type of fund.

Another approach would be to fit a fixed effects linear panel data model with an AR(1) disturbance or with panel-corrected standard errors.

• Thank you Mr. Dimitryi and Mr. Richard. I create a equal weight average portfolio with all the 148 funds. So I have to run an unit root test (stationarity), heteroskedasticity test and a serial correlation test? – D. Adams Jul 30 '16 at 15:00
• @Duarte It seems strange to me that you would average the funds. What is the reason for this? – Dimitriy V. Masterov Jul 30 '16 at 15:10
• My supervisor advice me to use a EWAP (Equal Weight Average Portfolio)... – D. Adams Jul 30 '16 at 15:29
• @Duarte I would edit your question with this key info. – Dimitriy V. Masterov Jul 30 '16 at 15:33

General remarks
If you want to assess all funds together, i.e. see if the seasonality is prevalent for all funds as a group, then follow Dimitriy's advice. If you would also like to inspect some funds separately, you could still use the regression you have. Just recall that by testing $n$ funds one by one, you would end up rejecting the null hypothesis of no seasonality $0.05 \times n$ times even when none of the funds were seasonal. Refer to the literature on multiple testing corrections then.

Testing for autocorrelation
Durbin-Watson test targets only first-order autocorrelation. For monthly returns on funds this could probably be sufficient; you could consult financial theory on whether higher-order autocorrelations could be expected. If checking higher-order autocorrelations were also of interest, you could use Breusch-Godfrey or Ljung-Box tests.

Conditional heteroskedasticity
You could also see if the model residuals have autoregressive conditional heteroskedasticity by using ARCH-LM test (ibid.). By neglecting heteroskedasticity when present, you could lose some power of your tests.