Description Usage Arguments Details Value Author(s) References See Also Examples
Invert (invertible) SARIMA(p, d, q, P, D, Q) models to ar representation.
1 2 |
notation |
"arima" for notation of the type used by the function arima(stats), "dse1" for type notation used by the package dse1. |
phi |
p vector of autoregressive coefficient. |
d |
difference operator, implemented: d element of (0,1,2). |
theta |
q vector of moving average coefficients. |
Phi |
P vector of seasonal autoregressive coefficients. |
D |
Seasonal difference operator, implemented: D element of (0,1,2). |
Theta |
Q vector of seasonal moving average coefficients. |
frequency |
The frequency of the seasonality (e.g. frequency = 12 for monthly series with annual periodicity). |
For input, positive values of phi, theta, Phi and Theta indicate positive dependence. Implemented for p,q,P,Q element of c(0,1,2,3,4,5,6,7,8,9,10). The ar representation is truncated at coefficients less than 1.0e-10. Values of theta, Theta near non invertibility (-1 or 1) will not be practical and will cause near infinite lags, especially for Theta and large frequency.
A vector containing a truncated autoregressive representation of a SARIMA model. This can be used as input for the function gar.sim.
Olivier Briet o.briet@gmail.com
Briet OJT, Amerasinghe PH, Vounatsou P: Generalized seasonal autoregressive integrated moving average models for count data with application to malaria time series with low case numbers. PLoS ONE, 2013, 8(6): e65761. doi:10.1371/journal.pone.0065761 https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0065761 If you use the gsarima package, please cite the above reference.
'garsim'.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 | phi<-c(0.5, 0.3, 0.1)
theta<-c(0.6, 0.2, 0.2)
ar<-arrep(phi=phi, theta=theta, frequency=12)
check<-(acf2AR(ARMAacf(ar=phi, ma=theta, lag.max = 100, pacf = FALSE))[100,1:length(ar)])
as.data.frame(cbind(ar,check))
phi<-c(0.2,0.5)
theta<-c(0.4)
Phi<-c(0.6)
Theta<-c(0.3)
d<-2
D<-1
frequency<-12
ar<-arrep(phi=phi, theta=theta, Phi=Phi, Theta=Theta, frequency= frequency, d=d, D=D)
N<-500
intercept<-10
data.sim <- garsim(n=(N+length(ar)),phi=ar, X=matrix(rep(intercept,(N+ length(ar)))),
beta=1, sd=1)
y<-data.sim[1+length(ar): (N+length(ar))]
tsy<-ts(y, freq= frequency)
plot(tsy)
arima(tsy, order=c(2,2,1), seasonal=list(order=c(1,1,1)))
|
ar check
1 1.100000e+00 1.100000e+00
2 -1.600000e-01 -1.600000e-01
3 1.760000e-01 1.760000e-01
4 -2.936000e-01 -2.936000e-01
5 1.729600e-01 1.729600e-01
6 -8.025600e-02 -8.025600e-02
7 7.228160e-02 7.228160e-02
8 -6.190976e-02 -6.190976e-02
9 3.874074e-02 3.874074e-02
10 -2.531881e-02 -2.531881e-02
11 1.982509e-02 1.982509e-02
12 -1.457944e-02 -1.457944e-02
13 9.846408e-03 9.846408e-03
14 -6.956975e-03 -6.956975e-03
15 5.120791e-03 5.120791e-03
16 -3.650361e-03 -3.650361e-03
17 2.557453e-03 2.557453e-03
18 -1.828558e-03 -1.828558e-03
19 1.315716e-03 1.315716e-03
20 -9.352089e-04 -9.352089e-04
21 6.636937e-04 6.636937e-04
22 -4.743177e-04 -4.743177e-04
23 3.388937e-04 3.388937e-04
24 -2.412114e-04 -2.412114e-04
25 1.718116e-04 1.718116e-04
26 -1.226234e-04 -1.226234e-04
27 8.745402e-05 8.745402e-05
28 -6.231005e-05 -6.231005e-05
29 4.441992e-05 4.441992e-05
30 -3.168074e-05 -3.168074e-05
31 2.258647e-05 2.258647e-05
32 -1.609972e-05 -1.609972e-05
33 1.147868e-05 1.147868e-05
34 -8.184562e-06 -8.184562e-06
35 5.834944e-06 5.834944e-06
36 -4.159791e-06 -4.159791e-06
37 2.965798e-06 2.965798e-06
38 -2.114509e-06 -2.114509e-06
39 1.507504e-06 1.507504e-06
40 -1.074760e-06 -1.074760e-06
41 7.662572e-07 7.662572e-07
42 -5.463031e-07 -5.463031e-07
43 3.894825e-07 3.894825e-07
44 -2.776803e-07 -2.776803e-07
45 1.979723e-07 1.979723e-07
46 -1.411438e-07 -1.411438e-07
47 1.006279e-07 1.006279e-07
48 -7.174243e-08 -7.174243e-08
49 5.114865e-08 5.114864e-08
50 -3.646628e-08 -3.646628e-08
51 2.599853e-08 2.599852e-08
52 -1.853559e-08 -1.853559e-08
53 1.321490e-08 1.321490e-08
54 -9.421530e-09 -9.421529e-09
55 6.717055e-09 6.717054e-09
56 -4.788908e-09 -4.788907e-09
57 3.414240e-09 3.414239e-09
58 -2.434173e-09 -2.434173e-09
59 1.735438e-09 1.735437e-09
60 -1.237276e-09 -1.237276e-09
61 8.821126e-10 8.821126e-10
62 -6.288999e-10 -6.289002e-10
63 4.483726e-10 4.483726e-10
64 -3.196661e-10 -3.196659e-10
65 2.279051e-10 2.279049e-10
66 -1.624844e-10 -1.624841e-10
67 1.158428e-10 1.158426e-10
Call:
arima(x = tsy, order = c(2, 2, 1), seasonal = list(order = c(1, 1, 1)))
Coefficients:
ar1 ar2 ma1 sar1 sma1
0.0246 0.6054 0.5072 0.6641 0.3021
s.e. 0.0957 0.0607 0.1156 0.0460 0.0606
sigma^2 estimated as 1.086: log likelihood = -719.44, aic = 1450.87
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