The Correlogram command computes autocorrelations of the data X and displays them as a column graph with dashed lines indicating the lower and upper 95% confidence bands for the normal distribution $N\left(0\,\frac{1}{L}\right)$, where L is the size of the sample X, and a caption reporting how many of the displayed columns lie outside of the bands of plus or minus 2, 3, and 4 standard deviations respectively.

The AutoCorrelationPlot command is provided as an alias.

$\mathrm{with}\left(\mathrm{Statistics}\right)\:$

$L≔\mathrm{LinearAlgebra}:-\mathrm{RandomVector}\left[\mathrm{row}\right]\left(10000\,\mathrm{generator}=0..1\right)$

$L≔\left[1\,1\,0\,1\,1\,1\,1\,1\,1\,1\,0\,0\,1\,1\,0\,0\,1\,1\,1\,1\,0\,0\,1\,1\,1\,0\,1\,0\,1\,1\,0\,1\,1\,1\,0\,0\,1\,1\,0\,0\,1\,1\,0\,1\,1\,1\,0\,0\,1\,1\,0\,1\,0\,0\,0\,1\,0\,0\,1\,1\,1\,1\,1\,1\,1\,1\,0\,1\,1\,0\,1\,1\,1\,0\,0\,1\,1\,1\,1\,1\,0\,0\,0\,0\,1\,1\,0\,1\,0\,1\,0\,1\,0\,1\,0\,0\,0\,1\,0\,0\,\dots \,\text{⋯ 9900 row vector entries not shown}\right]$

$\mathrm{Correlogram}\left(L\right)$

$\mathrm{Correlogram}\left(L\,\mathrm{lags}=100\right)$

$\mathrm{Correlogram}\left(L\,\mathrm{nocaption}\right)$

$R≔⟨\mathrm{seq}\left(\frac{1}{3}\left(\mathrm{evalf}\left(\sin \left(17.2i\right)\cos \left(13.8i\right)+1.17\right)+\frac{\mathrm{rand}\left(0..1\right)\left(\right)\cdot 2}{3}\right)\,i=1..500\right)⟩$

$R≔\begin{array}{c}\left[\begin{array}{c}0.5022924310\\ 0.3491554423\\ 0.3375294174\\ 0.3672458047\\ 0.3064373098\\ 0.4562948270\\ 0.4122422130\\ 0.7895597522\\ 0.5851758922\\ 0.6199950623\\ ⋮\end{array}\right]\\ \hfill \text{500 element Vector[column]}\end{array}$

$\mathrm{LineChart}\left(R\,\mathrm{size}=\left[0.5\,''golden''\right]\right)$

$\mathrm{Correlogram}\left(R\,\mathrm{lags}=100\right)$

$\mathrm{with}\left(\mathrm{TimeSeriesAnalysis}\right)\:$

$\mathrm{Data}≔\mathrm{Import}\left(''datasets/sunspots.csv''\,\mathrm{base}=\mathrm{datadir}\,\mathrm{output}=\mathrm{Matrix}\right)$

$\mathrm{Data}≔\begin{array}{c}\left[\begin{array}{cc}''Date''& ''Mean\; Sunspot\; Number''\\ 1700& 5.0\\ 1701& 11.0\\ 1702& 16.0\\ 1703& 23.0\\ 1704& 36.0\\ 1705& 58.0\\ 1706& 29.0\\ 1707& 20.0\\ 1708& 10.0\\ ⋮& ⋮\end{array}\right]\\ \hfill \text{315 × 2 Matrix}\end{array}$

$\mathrm{tsData}≔\mathrm{TimeSeries}\left(\mathrm{Data}\left[265..310,2\right]\right)$

$\mathrm{tsData}≔\left[\begin{array}{c}\mathrm{Time\; series}\\ \mathrm{data\; set}\\ \mathrm{46\; rows\; of\; data:}\\ \mathrm{1979\; -\; 2024}\end{array}\right]$

$\mathrm{Correlogram}\left(\mathrm{GetData}\left(\mathrm{tsData}\right)\right)$

The Statistics[Correlogram] command was introduced in Maple 2019.

For more information on Maple 2019 changes, see Updates in Maple 2019.