Testing Weekday Effects in Stock Returns

Summary

The question proposes a Markov switching autoregression in which the return intercept changes across regimes, then interprets those regimes as weekday or monthly effects. The answer cautions that an AR(1) model may not be a suitable description of stock returns. For a weekday hypothesis, it suggests a more direct regression with weekday indicator variables and the prior trading day’s return as a control. Each weekday coefficient then measures a conditional return difference relative to the omitted day.

The answer reports that, in its test of daily S&P 500 data since 1970, the weekday coefficients were not statistically distinguishable from zero. It also suggests comparing unconditional average returns across weekdays with a test of differences in means, expecting a similar conclusion. These are initial tests rather than evidence of a robust trading effect: the document gives no detailed diagnostics, monthly analysis, multiple-testing adjustment, or out-of-sample validation, and its reported result is limited to that particular dataset and specification.

Key ideas

• A switching intercept model does not by itself establish that regimes correspond to calendar effects.
• An AR(1) assumption for stock returns may be questionable and should be assessed.
• Weekday indicator regression can estimate conditional differences while controlling for the prior trading day’s return.
• An unconditional comparison of weekday mean returns provides a simpler complementary test.
• The reported S&P 500 test found no statistically significant weekday coefficients, but it is a limited specification and sample.

Tags

# Markov switching regime for stock returns


# Markov switching regime for stock returns












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 by phdstudent (score 2, accepted)

https://quant.stackexchange.com/a/39399

Two things to note:

- First you are assuming that stock returns follow some type of AR(1) which I do not think is a reasonable model;

- 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.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.