Testing For Autocorrelation – Durbin-Watson Test
Durbin Watson test is a statistical test use to detect the presence of autocorrelation in the residuals of a regression analysis. The value of DW statistic always ranges between 0 and 4.
In stock market, positive autocorrelation (when DW<2) in stock prices suggests that the price movements have a persistent trend. Positive autocorrelation indicates that the variable increased or decreased on a previous day, there is a there is a tendency for it to follow the same direction on the current day. For example, if the stock fell yesterday, there is a higher likelihood it will fall today. Whereas the negative autocorrelation (when DW>2) indicates that if a variable increased or decreased on a previous day, there is a tendency for it to move in the opposite direction on the current day. For example, if the stock fell yesterday, there is a greater likelihood it will rise today.
Assumptions for the Durbin-Watson Test:
- The errors are normally distributed, and the mean is 0.
- The errors are stationary.
Calculation of DW Statistics
Where et is the residual of error from the Ordinary Least Squares (OLS) method.
The null hypothesis and alternate hypothesis for the Durbin-Watson Test are:
- H0: No first-order autocorrelation in the residuals ( ρ=0)
- HA: Autocorrelation is present.
Formula of DW Statistics
[Tex]d = \frac{\sum_{t=2}^{T}(e_t – e_{t-1})^2}{\sum_{t=1}^{T}e_{t}^{2}} [/Tex]
Here,
- et is the residual at time t
- T is the number of observations.
Interpretation of DW Statistics
- If the value of DW statistic is 2.0, it suggests that there is no autocorrelation detected in the sample.
- If the value is less than 2, it suggests that there is a positive autocorrelation.
- If the value is between 2 and 4, it suggests that there is a negative autocorrelation.
Decision Rule
- If the Durbin-Watson test statistic is significantly different from 2, it suggests the presence of autocorrelation.
- The decision to reject the null hypothesis depends on the critical values provided in statistical tables for different significance levels.
AutoCorrelation
Autocorrelation is a fundamental concept in time series analysis. Autocorrelation is a statistical concept that assesses the degree of correlation between the values of variable at different time points. The article aims to discuss the fundamentals and working of Autocorrelation.
Table of Content
- What is Autocorrelation?
- What is Partial Autocorrelation?
- Testing For Autocorrelation – Durbin-Watson Test
- Need For Autocorrelation in Time Series
- Autocorrelation Vs Correlation
- Difference Between Autocorrelation and Multicollinearity
- How to calculate Autocorrelation in Python?
- How to Handle Autocorrelation?
- Frequently Asked Questions (FAQs)