Markov switching regime for stock returns

Question

I want to see if day of the week (or month) has some effect on stock returns. I want to use Markov switching model to identify different regimes in time series.

If $Y_1,Y_2,...Y_t$ are stock returns, I want to apply following model

$Y_t=a+bY_{t-1}$ and I will say that $a$ can change across regimes. So I will get for example that at some period stock returns follow this

$Y_t=a_1+bY_{t-1}$

or

$Y_t=a_2+bY_{t-1}$

or

$Y_t=a_3+bY_{t-1}$

And using this I will argue that at some days of the week or months stock return is higher. Do you think it is viable procedure?

Answer 1

Two things to note:

1. First you are assuming that stock returns follow some type of AR(1) which I do not think is a reasonable model;
2. Casting consideration (1) aside, you can estimate what you want by doing:

\begin{equation} Y_t = \alpha + \alpha_{mon} + \alpha_{tue} + \alpha_{wed} + \alpha_{thu} + b Y_{t-1} + error \end{equation}

This will give you a first hint on whether returns for different days of the week are indeed different. In particular the interpretation of the coefficient $alpha_{mon}$ would be: conditional on the return on the previous trading day how much higher is the return on a monday vs a friday.

If you estimate this regression all weekday coefficients are statistically zero (I tried it with daily data of the S&P500 since 1970).

Also, a more direct test would just be to check if returns are on average different depending on the day of the week. Just take unconditional means a make a t-test for differences in means. You will probably get the same answer.