Skip to contents

Compute autocovariances and periodic autocovariances

autocovariances-methods.Rd

Methods for the generic function autocovariances(), which computes autocovariances meaningful for the first argument. For objects representing time series, it computes sample autocovariances (univariate, multivariate, periodic, as appropriate). For objects representing models, it computes the relevant theoretical autocovariances.

Methods

signature(x = "numeric", maxlag = "ANY")

signature(x = "PeriodicArmaModel", maxlag = "ANY")

signature(x = "PeriodicArModel", maxlag = "ANY")

signature(x = "PeriodicAutocovarianceModel", maxlag = "ANY")

signature(x = "PeriodicTS", maxlag = "ANY")

signature(x = "VirtualPeriodicAutocovariances", maxlag = "ANY")

If maxlag is missing or equal to maxLag(x), x is returned unchanged. Otherwise the number of available lags is adjusted to maxlag.

See also

autocovariances in package sarima for further details.

autocorrelations for autocorrelations;

Examples

## periodic ts object => peridic acvf
autocovariances(pcts(AirPassengers), maxlag = 10)
#> An object of class "SamplePeriodicAutocovariances"
#> Slot "modelCycle":
#> Object from built-in class 'MonthYearCycle'
#> Cycle start: January 
#> 
#> Slot "data":
#> An object of class "Lagged2d"
#> Slot *data*: 
#>         Lag_0     Lag_1     Lag_2     Lag_3     Lag_4     Lag_5     Lag_6
#> Jan  9357.021  7281.135  6713.656  7601.193  8713.974 10982.141 10844.250
#> Feb  7362.333  8285.417  6416.792  5910.458  6684.146  7663.104  9657.688
#> Mar  9269.472  8193.417  9249.958  7053.391  6510.794  7389.061  8463.578
#> Apr 10568.576  9814.486  8774.667  9903.771  7687.529  7082.272  8013.427
#> May 12068.139 11274.181 10521.028  9379.250 10592.708  8169.873  7532.303
#> Jun 16513.722 14057.778 13143.611 12309.472 10996.500 12414.417  9596.676
#> Jul 22545.222 19260.694 16434.722 15358.556 14338.861 12819.000 14491.167
#> Aug 22246.076 22344.889 19122.194 16306.681 15215.326 14286.069 12746.000
#> Sep 14084.243 17653.632 17798.194 15228.222 12994.569 12141.715 11368.514
#> Oct 11242.410 12565.257 15773.868 15904.389 13596.278 11622.764 10859.701
#> Nov  8305.306  9649.014 10798.986 13553.264 13647.389 11677.361  9977.889
#> Dec  9742.639  8982.722 10435.431 11686.819 14632.597 14764.306 12612.778
#>         Lag_7     Lag_8     Lag_9    Lag_10
#> Jan  9390.208  7856.760  7194.995  7311.302
#> Feb  9545.917  8252.583  6892.292  6295.354
#> Mar 10690.235 10555.954  9178.907  7610.891
#> Apr  9157.685 11586.472 11421.185  9879.495
#> May  8538.140  9766.638 12372.091 12184.935
#> Jun  8846.787 10023.273 11494.366 14471.218
#> Jul 11223.935 10362.741 11751.505 13464.856
#> Aug 14391.271 11132.598 10300.258 11680.350
#> Sep 10132.167 11438.188  8774.117  8095.832
#> Oct 10129.903  9065.083 10235.146  7870.328
#> Nov  9302.014  8724.444  7776.417  8777.125
#> Dec 10777.472 10052.681  9414.111  8393.500
#> 
#> Slot "n":
#> [1] 144
#> 
#> Slot "varnames":
#> character(0)
#> 
#> Slot "objectname":
#> [1] "pcts(AirPassengers)"
#> 

## for "ts" or "numeric" objects the default is non-periodic acvf
autocovariances(AirPassengers, maxlag = 10) 
#> An object of class "SampleAutocovariances"
#>     Lag_0     Lag_1     Lag_2     Lag_3     Lag_4     Lag_5     Lag_6     Lag_7 
#> 14291.973 13549.467 12513.692 11529.066 10756.502 10201.181  9743.318  9474.212 
#>     Lag_8     Lag_9    Lag_10 
#>  9369.968  9589.176 10043.254 
#> Slot n:
#> [1] 144
#> Slot varnames:   <not set>
#> Slot objectname:  x
autocovariances(as.numeric(AirPassengers))
#> An object of class "SampleAutocovariances"
#>     Lag_0     Lag_1     Lag_2     Lag_3     Lag_4     Lag_5     Lag_6     Lag_7 
#> 14291.973 13549.467 12513.692 11529.066 10756.502 10201.181  9743.318  9474.212 
#>     Lag_8     Lag_9    Lag_10    Lag_11    Lag_12    Lag_13    Lag_14    Lag_15 
#>  9369.968  9589.176 10043.254 10622.369 10867.546 10185.330  9237.507  8374.002 
#>    Lag_16    Lag_17    Lag_18    Lag_19    Lag_20    Lag_21 
#>  7688.441  7142.378  6699.134  6429.540  6311.747  6534.630 
#> Slot n:
#> [1] 144
#> Slot varnames:   <not set>
#> Slot objectname:  x
## argument 'nseasons' forces periodic acvf
autocovariances(AirPassengers, maxlag = 10, nseasons = 12)
#> An object of class "SampleAutocovariances"
#>     Lag_0     Lag_1     Lag_2     Lag_3     Lag_4     Lag_5     Lag_6     Lag_7 
#> 14291.973 13549.467 12513.692 11529.066 10756.502 10201.181  9743.318  9474.212 
#>     Lag_8     Lag_9    Lag_10 
#>  9369.968  9589.176 10043.254 
#> Slot n:
#> [1] 144
#> Slot varnames:   <not set>
#> Slot objectname:  x
autocovariances(as.numeric(AirPassengers), maxlag = 10, nseasons = 12)
#> An object of class "SamplePeriodicAutocovariances"
#> Slot "modelCycle":
#> Object from class 'BareCycle'
#> Number of seasons:  
#> 
#> Slot "data":
#> An object of class "Lagged2d"
#> Slot *data*: 
#>         Lag_0     Lag_1     Lag_2     Lag_3     Lag_4     Lag_5     Lag_6
#> S1   9357.021  7281.135  6713.656  7601.193  8713.974 10982.141 10844.250
#> S2   7362.333  8285.417  6416.792  5910.458  6684.146  7663.104  9657.688
#> S3   9269.472  8193.417  9249.958  7053.391  6510.794  7389.061  8463.578
#> S4  10568.576  9814.486  8774.667  9903.771  7687.529  7082.272  8013.427
#> S5  12068.139 11274.181 10521.028  9379.250 10592.708  8169.873  7532.303
#> S6  16513.722 14057.778 13143.611 12309.472 10996.500 12414.417  9596.676
#> S7  22545.222 19260.694 16434.722 15358.556 14338.861 12819.000 14491.167
#> S8  22246.076 22344.889 19122.194 16306.681 15215.326 14286.069 12746.000
#> S9  14084.243 17653.632 17798.194 15228.222 12994.569 12141.715 11368.514
#> S10 11242.410 12565.257 15773.868 15904.389 13596.278 11622.764 10859.701
#> S11  8305.306  9649.014 10798.986 13553.264 13647.389 11677.361  9977.889
#> S12  9742.639  8982.722 10435.431 11686.819 14632.597 14764.306 12612.778
#>         Lag_7     Lag_8     Lag_9    Lag_10
#> S1   9390.208  7856.760  7194.995  7311.302
#> S2   9545.917  8252.583  6892.292  6295.354
#> S3  10690.235 10555.954  9178.907  7610.891
#> S4   9157.685 11586.472 11421.185  9879.495
#> S5   8538.140  9766.638 12372.091 12184.935
#> S6   8846.787 10023.273 11494.366 14471.218
#> S7  11223.935 10362.741 11751.505 13464.856
#> S8  14391.271 11132.598 10300.258 11680.350
#> S9  10132.167 11438.188  8774.117  8095.832
#> S10 10129.903  9065.083 10235.146  7870.328
#> S11  9302.014  8724.444  7776.417  8777.125
#> S12 10777.472 10052.681  9414.111  8393.500
#> 
#> Slot "n":
#> [1] 144
#> 
#> Slot "varnames":
#> character(0)
#> 
#> Slot "objectname":
#> [1] "as.numeric(AirPassengers)"
#>