X is the univariate time series data (a one dimensional array of cells (e.g. rows or columns)).

Order is the time order in the data series (i.e. the first data point's corresponding date (earliest date=1 (default), latest date=0)).

k is the lag order (e.g. 0=no lag, 1=1st lag, etc.). If missing, the default lag order of one (i.e. Lag=1) is assumed.

Method is the calculation method for estimating the autocorrelation (0= Sample Autocorrelation (Default), 2=Periodogram-based estimate , 2=Cross corelation).

rho is the assumed autocorrelation function value. If missing, the default of zero is assumed.

Return_type is a switch to select the return output (1 = P-Value (default), 2 = Test Stats, 3 = Critical Value.

Alpha is the statistical significance of the test (i.e. alpha). If missing or omitted, an alpha value of 5% is assumed.

1. The time series is homogeneous or equally spaced.
2. The time series may include missing values (e.g. #N/A) at either end.
3. The lag order (k) must be less than the time series size, or an error value (#VALUE!) is returned.
4. The test hypothesis for the population autocorrelation: $$H_{o}: \rho_{k}=\rho_o$$ $$H_{1}: \rho_{k}\neq a$$ Where:
   
   • $H_{o}$ is the null hypothesis.
   • $H_{1}$ is the alternate hypothesis.
   • $\hat \rho_o$ is the assumed population autocorrelation function for lag k.
   • $k$ is the lag order.
5. Assuming a normal distributed population, the sample autocorrelation has a normal distribution: $$\hat \rho_k \sim N(\rho_k,\sigma_{\rho_k}^2)$$ Where:
   
   • $\hat \rho_k $ is the sample autocorrelation for lag k.
   • $\rho_k $ is the population autocorrelation for lag k.
   • $\sigma_{\rho_k}$ is the standard deviation of the sample autocorrelation function for lag k.
6. The variance of the sample autocorrelation is computed as: $$ \sigma_{\rho_k}^2 = \frac{1+\sum_{j=1}^{k-1}\hat\rho_j^2}{T} $$ Where:
   
   • $\sigma_{\rho_k}$ is the standard error of the sample autocorrelation for lag k.
   • $T$ is the sample data size.
   • $\hat\rho_j$ is the sample autocorrelation function for lag j.
   • $k$ is the lag order.
7. This is a two-sides (i.e. two-tails) test, so the computed p-value should be compared with half of the significance level ($\alpha/2$).

Example 1:

Files Examples

Related Links

• Wikipedia - Confidence interval
• Wikipedia - Statistical hypothesis testing

References

• D. S.G. Pollock; Handbook of Time Series Analysis, Signal Processing, and Dynamics; Academic Press; Har/Cdr edition(Nov 17, 1999), ISBN: 125609906
• James Douglas Hamilton; Time Series Analysis; Princeton University Press; 1st edition(Jan 11, 1994), ISBN: 691042896
• Tsay, Ruey S.; Analysis of Financial Time Series; John Wiley & SONS; 2nd edition(Aug 30, 2005), ISBN: 0-471-690740
• Box, Jenkins and Reisel; Time Series Analysis: Forecasting and Control; John Wiley & SONS.; 4th edition(Jun 30, 2008), ISBN: 470272848
• Walter Enders; Applied Econometric Time Series; Wiley; 4th edition(Nov 03, 2014), ISBN: 1118808568