Econometric Theory Serial Correlation Wikibooks, open books for an open world

Moreover, a course in regression is generally a prerequisite for any time series course, so it is helpful to at least provide exposure to some of the more commonly studied time series techniques. One thing to note about the Cochrane-Orcutt approach is that it does not always work properly. This occurs primarily because if the errors are positively autocorrelated, then r tends to underestimate \(\rho\).

  1. If we had ignored the autocorrelation in the residuals, we could consider the coefficient significant.
  2. Unit root processes, trend-stationary processes, autoregressive processes, and moving average processes are specific forms of processes with autocorrelation.
  3. A correlogram shows the correlation of a series of data with itself; it is also known as an autocorrelation plot and an ACF plot.
  4. The quantity supplied in the period $t$ of many agricultural commodities depends on their price in period $t-1$.
  5. Conversely, negative autocorrelation represents that the increase observed in a time interval leads to a proportionate decrease in the lagged time interval.

Autocorrelation can cause problems in conventional analyses (such as ordinary least squares regression) that assume independence of observations. The observations with positive autocorrelation can be plotted into a smooth curve. By adding a regression line, it can be observed that a positive error is followed by another positive one, and a negative error is followed by another negative one. It ranges from -1 (perfectly negative autocorrelation) to 1 (perfectly positive autocorrelation). Positive autocorrelation means that the increase observed in a time interval leads to a proportionate increase in the lagged time interval.

Autocorrelation- Concept, Causes and Consequences

Multicollinearity occurs when independent variables are correlated and one can be predicted from the other. An example of autocorrelation includes measuring the weather for a city on June 1 and the weather for the same city on June 5. Multicollinearity measures the correlation of two independent variables, such as a person’s height and weight.

Hildreth-Lu Procedure

The Cochrane–Orcutt procedure is a method famous in econometrics and in a variety of areas to address issues of autocorrelation in a time series through a linear model for serial correlation in the error term [1,2]. We already know that this violates one of the assumptions of ordinary least squares (OLS) regression, which assumes that the errors (residuals) are uncorrelated [1]. Later in the article, we’re going to use the procedure to remove autocorrelation and check how biased the coefficients are. In this regression model, the response variable in the previous time period has become the predictor and the errors have our usual assumptions about errors in a simple linear regression model.

If the temperature values that occurred closer together in time are, in fact, more similar than the temperature values that occurred farther apart in time, the data would be autocorrelated. Autocorrelation is the correlation of a time series and its lagged version over time. Although similar to correlation, autocorrelation uses the same time series twice. Financial analysts and traders use autocorrelation to examine historical price movements and predict future ones. Technical analysts use autocorrelation to determine what or how much of an impact historical prices of a security have on its future price.


Autocorrelation can help determine if there is a momentum factor at play with a given stock. If a stock with a high positive autocorrelation posts two straight days of big gains, for example, it might be reasonable to expect the stock to rise over the next two days, as well. On the other hand, an autocorrelation of -1 represents a perfect negative correlation (an increase seen in one time series results in a proportionate decrease in the other time series). An autocorrelation of +1 represents a perfect positive correlation (an increase seen in one time series leads to a proportionate increase in the other time series). For example, if it’s rainy today, the data suggests that it’s more likely to rain tomorrow than if it’s clear today. When it comes to investing, a stock might have a strong positive autocorrelation of returns, suggesting that if it’s “up” today, it’s more likely to be up tomorrow, too.

Without getting too technical, the Durbin-Watson is a statistic that detects autocorrelation from a regression analysis. Both the FCSNet and ImFCSNet based methods are more precise than traditional FCS methods in terms of diffusion coefficients, but they have different trade-offs for data requirements and spatial resolution. By utilizing less data, these techniques can potentially shorten the evaluation time by orders of magnitude, especially for large datasets or complex systems. Now the autocorrelation of the residuals was removed and the estimate is not biased anymore. If we had ignored the autocorrelation in the residuals, we could consider the coefficient significant.

It is necessary to test for autocorrelation when analyzing a set of historical data. For example, in the equity market, the stock prices on one day can be highly correlated to the prices on another day. However, it provides little information for statistical data analysis and does not tell the actual performance of the stock. Correlation measures the relationship between two variables, whereas autocorrelation measures the relationship of a variable with lagged values of itself.

In a regression analysis, autocorrelation of the regression residuals can also occur if the model is incorrectly specified. For example, if you are attempting to model a simple linear relationship but the observed relationship is non-linear (i.e., it follows a curved or U-shaped function), then the residuals will be autocorrelated. Conversely, negative autocorrelation represents that the increase observed causes of autocorrelation in a time interval leads to a proportionate decrease in the lagged time interval. By plotting the observations with a regression line, it shows that a positive error will be followed by a negative one and vice versa. It is common practice in some disciplines (e.g. statistics and time series analysis) to normalize the autocovariance function to get a time-dependent Pearson correlation coefficient.

Statistical software such as SPSS may include the option of running the Durbin-Watson test when conducting a regression analysis. Values close to 2 (the middle of the range) suggest less autocorrelation, and values closer to 0 or 4 indicate greater positive or negative autocorrelation respectively. If the price of a stock with strong positive autocorrelation has been increasing for several days, the analyst can reasonably estimate the future price will continue to move upward in the recent future days.

We can see in this plot that at lag 0, the correlation is 1, as the data is correlated with itself. At a lag of 1, the correlation is shown as being around 0.5 (this is different to the correlation computed above, as the correlogram uses a slightly different formula). We can also see that we have negative correlations when the points are 3, 4, and 5 apart. When mean values are subtracted from signals before computing an autocorrelation function, the resulting function is usually called an auto-covariance function. The auto part of autocorrelation is from the Greek word for self, and autocorrelation means data that is correlated with itself, as opposed to being correlated with some other data.

Over 1.8 million professionals use CFI to learn accounting, financial analysis, modeling and more. Start with a free account to explore 20+ always-free courses and hundreds of finance templates and cheat sheets. Autocorrelation can be used in many disciplines but is often seen in technical analysis. Technical analysts evaluate securities to identify trends and make predictions about their future performance based on those trends. Therefore, Rain can adjust their portfolio to take advantage of the autocorrelation, or momentum, by continuing to hold their position or accumulating more shares.

Where the data has been collected across space or time, and the model does not explicitly account for this, autocorrelation is likely. For example, if a weather model is wrong in one suburb, it will likely be wrong in the same way in a neighboring suburb. The fix is to either include the missing variables, or explicitly model the autocorrelation (e.g., using an ARIMA model). Sampling error alone means that we will typically see some autocorrelation in any data set, so a statistical test is required to rule out the possibility that sampling error is causing the autocorrelation. This test only explicitly tests first order correlation, but in practice it tends to detect most common forms of autocorrelation as most forms of autocorrelation exhibit some degree of first order correlation. A correlogram shows the correlation of a series of data with itself; it is also known as an autocorrelation plot and an ACF plot.