[2] | 1 | ; $Id$ |
---|
| 2 | ; Copyright (c) 1995-1997, Research Systems, Inc. All rights reserved. |
---|
| 3 | ; Unauthorized reproduction prohibited. |
---|
| 4 | ;+ |
---|
| 5 | ; NAME: |
---|
| 6 | ; a2_correlate |
---|
| 7 | ; |
---|
| 8 | ; PURPOSE: |
---|
| 9 | ; This function computes the autocorrelation Px(L) or autocovariance |
---|
| 10 | ; Rx(L) of a sample population X as a function of the lag (L). |
---|
| 11 | ; |
---|
| 12 | ; CATEGORY: |
---|
| 13 | ; Statistics. |
---|
| 14 | ; |
---|
| 15 | ; CALLING SEQUENCE: |
---|
| 16 | ; Result = A_correlate(X, Lag) |
---|
| 17 | ; |
---|
| 18 | ; INPUTS: |
---|
| 19 | ; X: An n-element vector of type integer, float or double. |
---|
| 20 | ; |
---|
| 21 | ; LAG: A scalar or n-element vector, in the interval [-(n-2), (n-2)], |
---|
| 22 | ; of type integer that specifies the absolute distance(s) between |
---|
| 23 | ; indexed elements of X. |
---|
| 24 | ; |
---|
| 25 | ; KEYWORD PARAMETERS: |
---|
| 26 | ; COVARIANCE: If set to a non-zero value, the sample autocovariance |
---|
| 27 | ; is computed. |
---|
| 28 | ; |
---|
| 29 | ; DOUBLE: If set to a non-zero value, computations are done in |
---|
| 30 | ; double precision arithmetic. |
---|
| 31 | ; |
---|
| 32 | ; EXAMPLE |
---|
| 33 | ; Define an n-element sample population. |
---|
| 34 | ; x = [3.73, 3.67, 3.77, 3.83, 4.67, 5.87, 6.70, 6.97, 6.40, 5.57] |
---|
| 35 | ; |
---|
| 36 | ; Compute the autocorrelation of X for LAG = -3, 0, 1, 3, 4, 8 |
---|
| 37 | ; lag = [-3, 0, 1, 3, 4, 8] |
---|
| 38 | ; result = a_correlate(x, lag) |
---|
| 39 | ; |
---|
| 40 | ; The result should be: |
---|
| 41 | ; [0.0146185, 1.00000, 0.810879, 0.0146185, -0.325279, -0.151684] |
---|
| 42 | ; |
---|
| 43 | ; PROCEDURE: |
---|
| 44 | ; See computational formula published in IDL manual. |
---|
| 45 | ; |
---|
| 46 | ; REFERENCE: |
---|
| 47 | ; INTRODUCTION TO STATISTICAL TIME SERIES |
---|
| 48 | ; Wayne A. Fuller |
---|
| 49 | ; ISBN 0-471-28715-6 |
---|
| 50 | ; |
---|
| 51 | ; MODIFICATION HISTORY: |
---|
| 52 | ; Written by: GGS, RSI, October 1994 |
---|
| 53 | ; Modified: GGS, RSI, August 1995 |
---|
| 54 | ; Corrected a condition which excluded the last term of the |
---|
| 55 | ; time-series. |
---|
| 56 | ; Modified: GGS, RSI, April 1996 |
---|
| 57 | ; Simplified AUTO_COV function. Added DOUBLE keyword. |
---|
| 58 | ; Modified keyword checking and use of double precision. |
---|
| 59 | ; Modified: W. Biagiotti, Advanced Testing Technologies Inc., Hauppauge, NY, July 1997 |
---|
| 60 | ; Moved all constant calculations out of main loop for greatly |
---|
| 61 | ; reduced processing time. |
---|
| 62 | ; |
---|
| 63 | ; DISCLAIMER: This routine has been modified from its original form as it was |
---|
| 64 | ; supplied by Research Systems, Inc (RSI). As such, RSI is not responsible |
---|
| 65 | ; for any errors existing in this code. |
---|
| 66 | ;- |
---|
| 67 | |
---|
| 68 | FUNCTION Auto_Cov, X, M, nX, Double = Double |
---|
| 69 | |
---|
| 70 | COMMON data, Xmean |
---|
| 71 | |
---|
| 72 | ;Sample autocovariance function. |
---|
| 73 | RETURN, TOTAL((X[0:nX - M] - Xmean) * (X[M:nX] - Xmean), Double = Double) |
---|
| 74 | |
---|
| 75 | END |
---|
| 76 | |
---|
| 77 | FUNCTION a2_correlate, X, Lag, Covariance = Covariance, Double = Double |
---|
| 78 | |
---|
| 79 | COMMON data, Xmean |
---|
| 80 | |
---|
| 81 | ;Compute the sample-autocorrelation or autocovariance of (Xt, Xt+l) |
---|
| 82 | ;as a function of the lag (l). |
---|
| 83 | |
---|
| 84 | ON_ERROR, 2 |
---|
| 85 | |
---|
| 86 | TypeX = SIZE(X) |
---|
| 87 | nX = TypeX[TypeX[0]+2] |
---|
| 88 | |
---|
| 89 | ;Check length. |
---|
| 90 | if nX lt 2 then $ |
---|
| 91 | MESSAGE, "X array must contain 2 or more elements." |
---|
| 92 | |
---|
| 93 | ;If the DOUBLE keyword is not set then the internal precision and |
---|
| 94 | ;result are identical to the type of input. |
---|
| 95 | if N_ELEMENTS(Double) eq 0 then $ |
---|
| 96 | Double = (TypeX[TypeX[0]+1] eq 5) |
---|
| 97 | |
---|
| 98 | nLag = N_ELEMENTS(Lag) |
---|
| 99 | |
---|
| 100 | if nLag eq 1 then Lag = [Lag] ;Create a 1-element vector. |
---|
| 101 | |
---|
| 102 | if Double eq 0 then Auto = FLTARR(nLag) else Auto = DBLARR(nLag) |
---|
| 103 | |
---|
| 104 | ; Calculate constants OUTSIDE of main loop |
---|
| 105 | Xmean = TOTAL(X, Double = Double) / nX |
---|
| 106 | nX = nX - 1 ; Translate into last index (avoid redundancy) |
---|
| 107 | last_idx = nLag - 1 ; Last loop indice |
---|
| 108 | Lag = ABS(Lag) ; Calculate with vector ops |
---|
| 109 | |
---|
| 110 | if KEYWORD_SET(Covariance) eq 0 then begin ;Compute Autocorrelation. |
---|
| 111 | |
---|
| 112 | for k = 0, last_idx do $ |
---|
| 113 | Auto[k] = Auto_Cov(X, Lag[k], nX, Double = Double) |
---|
| 114 | |
---|
| 115 | temp_Corr = Auto_Cov(X, 0L, nX, Double = Double) |
---|
| 116 | Auto = Auto / temp_Corr |
---|
| 117 | |
---|
| 118 | endif else begin ;Compute Autocovariance. |
---|
| 119 | for k = 0, last_idx do $ |
---|
| 120 | Auto[k] = Auto_Cov(X, Lag[k], nX, Double = Double) |
---|
| 121 | |
---|
| 122 | Auto = Auto / nX |
---|
| 123 | endelse |
---|
| 124 | |
---|
| 125 | if Double eq 0 then RETURN, FLOAT(Auto) else $ |
---|
| 126 | RETURN, Auto |
---|
| 127 | |
---|
| 128 | END |
---|