Higher-Order Autocorrelation & Correlogram | Time Series Econometrics

In this lesson, we extend the analysis of autocorrelation beyond lag one and introduce the **correlogram**, an essential tool in time-series econometrics. Using a simulated GDP growth rate for an assumed economy, we calculate sample autocorrelations at different lags, examine how persistence declines over time, and visualize the resulting autocorrelation pattern in a correlogram. We also introduce approximate *5% significance bounds* and interpret which autocorrelations provide evidence of statistically significant serial correlation. What you will learn: What higher-order autocorrelation means The meaning of lag 1, lag 2, lag 3, and higher-order lags The general formula for the sample autocorrelation at lag s How to calculate autocorrelations using Mathematica How autocorrelation changes as the lag increases How to construct and interpret a correlogram How to interpret positive, near-zero, and negative autocorrelation How approximate 5% significance bounds are calculated How the shape of a correlogram reveals persistence and serial dependence Example: For the simulated GDP growth series, the autocorrelations are: Lag 1: 0.740 Lag 2: 0.542 Lag 3: 0.392 Lag 4: 0.276 Lag 5: 0.187 Lag 6: 0.117 Lag 7: 0.063 Lag 8: 0.020 Lag 9: −0.015 Lag 10: −0.044 The pattern shows strong positive autocorrelation at short lags, followed by a gradual decline toward zero. With approximate 5% significance bounds of ±0.358, the first three autocorrelations lie outside the bounds, providing evidence of positive serial correlation at lags 1 through 3 in this simulated example. Chapters 00:00 Introduction: From Lag-One to Higher-Order Autocorrelation 00:27 Simulated GDP Growth and Persistence 01:07 Understanding Lag 1, Lag 2, and Lag 3 01:52 Sample Autocorrelation at Lag s 02:56 Building the Autocorrelation Function in Mathematica 03:22 Calculating Higher-Order Autocorrelations 03:57 Interpreting the Autocorrelation Sequence 04:45 Introducing the Correlogram 05:00 Reading and Interpreting the Correlogram 06:30 Adding 5% Significance Bounds 07:14 Testing Autocorrelations Against the Bounds 08:02 Interpreting the Shape of a Correlogram Related topics This lesson is part of a time-series econometrics sequence covering autocorrelation, persistence, sample autocorrelation, and correlograms. #Econometrics #TimeSeries #Autocorrelation #Correlogram #GDPGrowth #Mathematica #Statistics #Economics #TimeSeriesEconometrics #SerialCorrelation