Autocorrelation in Time Series Data

Why Time Series Data Is Unique

A time series is a series of data points indexed in time. The fact that time series data is ordered makes it unique in the data space because it often displays serial dependence序列依赖. Serial dependence occurs when the value of a datapoint at one time is statistically dependent on another datapoint in another time. However, this attribute of time series data violates违反 one of the fundamental assumptions of many statistical analyses — that data is statistically independent.

What Is Autocorrelation?

Autocorrelation is a type of serial dependence. Specifically, autocorrelation is when a time series is linearly related to a lagged version of itself. By contrast, correlation is simply when two independent variables are linearly related.

Why Autocorrelation Matters

Often, one of the first steps in any data analysis is performing regression analysis. However, one of the assumptions of regression analysis is that the data has no autocorrelation. This can be frustrating because if you try to do a regression analysis on data with autocorrelation, then your analysis will be misleading.

Additionally, some time series forecasting methods (specifically regression modeling) rely on the assumption that there isn’t any autocorrelation in the residuals (the difference between the fitted model and the data). People often use the residuals to assess whether their model is a good fit while ignoring that assumption that the residuals have no autocorrelation (or that the errors are independent and identically distributed or i.i.d). This mistake can mislead people into believing that their model is a good fit when in fact it isn’t. I highly recommend reading this article about How (not) to use Machine Learning for time series forecasting: Avoiding the pitfalls in which the author demonstrates how the increasingly popular LSTM (Long Short Term Memory) Network can appear to be an excellent univariate time series predictor, when in reality it’s just overfitting the data. He goes further to explain how this misconception is the result of accuracy metrics failing due to the presence of autocorrelation.

Finally, perhaps the most compelling aspect of autocorrelation analysis is how it can help us uncover hidden patterns in our data and help us select the correct forecasting methods. Specifically, we can use it to help identify seasonality and trend in our time series data. Additionally, analyzing the autocorrelation function (ACF) and partial autocorrelation function (PACF) in conjunction is necessary for selecting the appropriate ARIMA model for your time series prediction.

How to Determine if Your Time Series Data Has Autocorrelation by python

For this exercise, I’m using InfluxDB and the InfluxDB Python CL. I am using available data from the National Oceanic and Atmospheric Administration’s (NOAA) Center for Operational Oceanographic Products and Services. Specifically, I will be looking at the water levels and water temperatures of a river in Santa Monica.

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