autocor¶
Purpose¶
Computes specified autocorrelations for each column of a matrix.
Format¶
-
a = autocor(x, k_f, k_l); - Parameters
x (NxK matrix) – Autocorrelations will be computed for each column separately. x is assumed to have 0 mean.
k_f (scalar) – Denotes first autocorrelation to compute. Range \([0, rows(x) -1]\).
k_l (scalar) – Denotes the last autocorrelation lags. Must be less than the number of rows of x. Range \([0, rows(x) -1]\). If \(k_f = 0\) and \(k_l = 0\), then all possible correlations are computed. If \(k_f \lt 0\) and \(k_l = 0\) then the zero order correlation is computed.
- Returns
a (matrix) – The autocorrelations for each column of x. Missing values will be returned if the variance of any variable is
0.
Examples¶
Example 1: Calculate ACF for a vector¶
new;
cls;
library tsmt;
// Step 1: Use 'acf' function as a comparison
// Import time series data
// Get file name with full path
fname = getGAUSSHome() $+ "examples/beef_prices.csv";
// Import beef price data
beef = loadd(fname, "beef_price");
// Demean beef price data first
bfdm = beef - meanc(beef);
// Define first lag for acf , 0 ≤ k_f ≤ N-1
k_f = 1;
// Define last lag for acf, 0 ≤ k_l ≤ N-1
k_l = 5;
// Compute ACF for demeaned beef price
a = autocor(bfdm, k_f, k_l);
// Print results
print "ACF from autocor function: ";
print "Lag"$~"ACF";
print seqa(k_f,1, k_l - k_f + 1)~a;
The results:
ACF from autocor function:
Lag ACF
1.0000000 0.98474980
2.0000000 0.96196414
3.0000000 0.94023737
4.0000000 0.92037936
5.0000000 0.90134772
Example 2: Calculate ACF for a matrix¶
// Set up a random seed
rndseed 22;
// Simulate a data set
x = rndn(10, 5);
// Demean data first
x = x - meanc(x)';
// Define first lag, k_f
k_f = 1;
// Define last lag, k_l
k_l = 6;
// Call autocor function
a = autocor(x, k_f, k_l);
// Print results
print "ACF for each column in the matrix";
print "Lag"$~"ACF of C_1"$~"ACF of C_2"$~"ACF of C_3"$~"ACF of C_4"$~"ACF of C_5";
print seqa(k_f,1, k_l - k_f + 1)~a;
The results are:
ACF for each column in the matrix
Lag ACF of C_1 ACF of C_2 ACF of C_3 ACF of C_4 ACF of C_5
1.0000000 -0.23535560 -0.23233084 -0.43327598 -0.12392805 0.46121428
2.0000000 -0.13586178 0.32137672 0.014887577 -0.49854290 0.0097333377
3.0000000 -0.097818783 -0.095531616 0.021427194 0.054173501 -0.14611108
4.0000000 0.24352134 -0.33590273 -0.12080847 0.29314286 0.019374906
5.0000000 -0.24234876 0.15793212 -0.049016036 -0.13335620 0.013169333
6.0000000 -0.090657186 -0.36787111 -0.040987953 -0.37958321 -0.13512905
Remarks¶
The data are assumed to have 0 mean. Thus, use:
x = x - meanc(x)';
prior to the use of this function if the mean is not 0.
Library¶
tsmt