# Serial Correlation

Last Updated :

21 Aug, 2024

Blog Author :

N/A

Edited by :

Ashish Kumar Srivastav

Reviewed by :

Dheeraj Vaidya

Table Of Contents

## What Is Serial Correlation?

Serial correlation is a term in statistics that depicts the correlation or relationship between the current value of a variable and the same variable’s lagged value from the previous periods. It is also known as autocorrelation, and this measure allows financial analysts to predict future movements in asset prices.

This correlation studies the past price movements in a security, like a stock or other financial instruments. If the present value of an asset is estimated to be serially correlated with the asset’s previous values, then the correlation can be employed to calculate the potential future values.

##### Table of Contents

- Serial correlation is a statistical instrument that enables financial analysts to study the previous price movements in a security’s prices and use the information to forecast future trends in the security prices.
- Commonly known as autocorrelation, this measure can be divided into several types. They are first-order correlation, second-order correlation, positive correlation, and negative correlation.
- This correlation type is a valuable tool for enhancing the accuracy of financial models. Furthermore, this estimate helps investors reduce the potential risks associated with an investment and maximize the returns on the investments.

### Serial Correlation In Financial Modeling Explained

Serial correlation is a statistical concept that establishes a relationship or correlation between a variable’s present value and the lagged value of the same variable from past periods. Also referred to as autocorrelation, this calculation studies the previous price movements of securities and utilizes the data to predict the securities’ future price trends. It enables investment analysts to predict the potential movement patterns of asset prices in the financial market.

Employing serial correlation tests while detecting, building, and implementing financial models started becoming prevalent with the increase in the usage of computer technology in the 1980s. In the current scenario, financial institutions, such as investment banks, make widespread use of autocorrelations. It allows them to enhance predictive models for investment returns by identifying trends that may take place in price movements over a period. This correlation aids in developing the accuracy of financial models. It also assists in reducing investment risks and maximizing investment returns.

### Types

The serial correlation types are as follows:

**First-order correlation:**This autocorrelation type results from the correlation between the error terms of adjacent periods instead of two or more previous periods. It is the most common form of autocorrelation. This type can be further divided into two types, which are positive and negative correlation.**Second-order correlation:**In this type, an error term impacts the data after two time periods.**Negative correlation:**This autocorrelation type takes place if a positive error for one event increases the possibility of a negative error for another event. In this type, the positive error in one period will result in a negative error in the next period. Conversely, if there is a negative error in one period, the odds of having a positive error in the next period are high.**Positive correlation:**In the positive serial correlation type, the positive error in one observation increases the odds of a positive error in another observation. As a result, if a positive error exists in one period, there is a high chance of a positive error existing in the next period. Furthermore, if there is a negative error in one event, the odds of experiencing a negative error in another event are high.

### How To Measure?

In financial models, serial correlations are of two types, which are positive and negative. A positive autocorrelation depicts that the value changes between an asset’s current price and future prices tend to be similar to the value changes between the previous prices and recent prices. However, a negative autocorrelation shows that the value changes between the current price of an asset and the asset’s future prices can move in opposite directions as the value changes between the previous prices and recent prices.

When an asset’s current price’s variable and its price at a previous period display positive autocorrelation, it indicates mean aversion. Mean aversion represents that the price changes in the asset are likely to follow trends. Over time, they will reflect higher standard deviation than in cases where there is no correlation. Autocorrelations are mostly calculated with values ranging from -1 to +1. A serial correlation test value with zero depicts there is no correlation. It indicates that there is no visible pattern existing between a variable’s current value and its value during past periods. Moreover, values nearer to +1 reflect positive autocorrelation, whereas values nearer to -1 reflect negative autocorrelation.

### Examples

Let us study the following serial correlation examples to understand this concept:

#### Example #1

Suppose Ryan is a financial analyst. He is studying an asset’s daily returns for 30 days. Ryan calculated the autocorrelation to determine if there was a significant link between the asset’s returns in the successive trading days. The results indicated a positive correlation. It suggested that the positive returns on the asset prices on one day are more likely to be followed by another positive return on the subsequent day. This pattern reflected a momentum in the asset’s market performance. This is a serial correlation example.

#### Example #2

A new study revealed that ChatGPT can accurately predict movements in stock prices. The AI tool can even replace investment analysts. In the study, more than 50,000 news data about companies dating back to October 2021 were entered into the ChatGPT chatbox. The tool assessed if the news was terrible, exemplary, or unrelated to the company’s stock prices. It also created a ChatGPT score that helped evaluate if it could predict the company’s stock market performance the next day. The study found that there was a substantial positive correlation between the ChatGPT score and the company’s stock market performance the following day.

### Effects

Autocorrelation does not create bias in the regression coefficient calculations. However, a positive serial correlation will expand the F-statistic to asses the overall importance of the regression. This impact occurs as the mean squared error (MSE) is prone to underestimate the population error variance. It results in the rise of Type I errors, which rejection of the null hypothesis even though it is true. This implies that users tend to reject the null hypothesis, although it is true if a positive correlation is present in the data.

Additionally, a negative serial correlation will diminish the F-statistic because the mean squared error is likely to overvalue the population error variance. This occurrence reduces the Type I errors but increases the Type II errors where users fail to reject the null hypothesis even if it is false. It implies the possibility of not rejecting the null hypothesis, although it is false, is high if there is a negative autocorrelation in the data.

### Frequently Asked Questions (FAQs)

**How to fix serial correlation?**

The Hansen method is one of the most popular techniques to fix this correlation. It suggests that the evaluation of the degree of this correlation in the data under review is the initial step in fixing this correlation. Additionally, altering the regression equation can also assist in correcting this correlation. This technique employs adding a lag term that depicts the dependent variable’s value at a previous period.

**How do we deal with serial correlation in panel data?**

This correlation is a severe issue in panel data. The presence of significant autocorrelation in the error term will make the standard errors inconsistent. Adjusting the standard errors to consider the autocorrelation is a standard approach to deal with this concern.

**Is serial correlation unit root?**

Unit root test is a testing method in statistics that aids in determining if a time series variable is not stationary and carries a unit root. Usually, the null hypothesis is expressed as the presence of a unit root. Conversely, the alternative hypothesis indicates trend stationarity, stationarity, or explosive root based on the test employed. Unit tests are closely related to autocorrelation, as all processes with a unit root will display autocorrelation. However, not all autocorrelated time series will possess a unit root.

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