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?

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

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  • $\begingroup$ 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? $\endgroup$ – D. Adams Jul 30 '16 at 15:00
  • $\begingroup$ @Duarte It seems strange to me that you would average the funds. What is the reason for this? $\endgroup$ – Dimitriy V. Masterov Jul 30 '16 at 15:10
  • $\begingroup$ My supervisor advice me to use a EWAP (Equal Weight Average Portfolio)... $\endgroup$ – D. Adams Jul 30 '16 at 15:29
  • $\begingroup$ @Duarte I would edit your question with this key info. $\endgroup$ – 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.

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