Grey-Markov method in R - r

In R, I have loaded the built-in time series: AirPassengers and split it in train- and testdata like this:
rm(list = ls())
data = AirPassengers
traindata = ts(data[1:(0.75*length(data))], frequency = 12)
testdata = ts(data[((0.75*length(data))+1):length(data)], frequency = 12)
from here I want to estimate future values of a time series with the traindata using the Grey-Markov method. I know the Grey-Markov method consist of a Grey GM(1, 1) forecasting model followed by a Markov chain forecasting model refinement. But is there a function in R that performs this Grey-Markov method on its own, just like, for example, the auto.arima function?

Related

Simulating multivariate time series in R

Suppose I have the following dataset:
"beta1","beta2","beta3","beta4","beta5","beta6"
1.90478635314552,-0.370299399555972,0.183593016388983,-0.434842981814434,-0.230143383561756,-0.190872066510384
1.00134375146289,0.140458122070579,-0.225094922401189,-0.156316834537037,-0.309451747023308,-0.0311491683843711
0.424245706523012,0.19510900677966,-0.324049413370315,-0.0795094444442133,-0.132633683802251,0.0481600792392325
-0.381486378300193,0.382988069609516,0.227590550359034,-0.140552762560857,0.228684259713061,0.324146768316466
-0.979361646454991,0.314682474902746,0.521104272103664,0.126760596547812,0.0927225402550753,0.300934105806576
-1.62693811337159,0.280342497461363,0.800305559431661,0.683348530693696,0.0522130203738253,-0.268561144651366
-2.36148919498382,0.309568482586132,0.841304046466423,0.779789307366862,-0.0974528558354508,-0.545068955874475
-1.2724465226541,-0.977075911542538,0.0868400529314154,0.458584034184093,0.384500428752736,-0.290766998398563
2.05128710252935,-0.343294002552086,0.20583226826602,-0.404816429182371,-0.168213357044999,-0.175191002159614
1.28420575697985,-0.0399245122056259,-0.0918277389261692,-0.122462550617879,-0.282482671856113,-0.0213169859672286
0.63841286347079,0.158963145242457,-0.329025611403002,0.0251271710043792,-0.152766852192694,0.0604744630683282
-0.125518941951678,0.345991408275115,-0.117345282624525,-0.109932180902408,0.193507682707975,0.0783939173344958
-0.765315571116247,0.355895150464671,0.114662459940379,-0.154653225249409,0.161233917523313,0.189081142865184
-1.46333424323841,0.321886354239832,0.557029796984241,0.20565360503893,-0.0470811308368904,0.126846340614928
-2.15819930360235,0.303417631035377,0.703191230200232,0.384213941018177,-0.188836533972588,-0.120188976189018
-1.4358194260921,-1.02983480072707,0.0700690319405454,0.349832739241328,0.266917878656354,-0.207093960877208
I fit multivariate time series model into the data using VAR function from the vars package:
var_model <- vars::VAR(data, p = 2, type = 'const')
Then how do I use this fitted model to simulate new multivariate time series in R?

How to decide the frequency while using the forecast function in R?

I have a series of daily data from 01-01-2014 to 31-01-2022. I want to predict the next 30 days. I am using auto.arima and it has some exogenous variables attached.
Here's the code: -
datax$NMD1<-(datax$NMD1/1000000000)
#Here to make an Arima series out of NMD 1. Exogenous variables here.
ts1<- ts(datax, frequency = 1)
class(ts1)
colnames(ts1)
autoplot(ts1[,"NMD1"])
#defining the set of exogenous variables
xset<- as.matrix(ts1[,"1Y TD INTEREST RATE"], ts1[,"BSE"], ts1[,"Repo Rate"], ts1[,"MIBOR Rate"], ts1[,"1Y OIS Rate" ], ts1[,"3M CD rate(PSU)"], ts1[,"2 Y GSec Rate"])
#Fitting the model
model1 <- auto.arima(ts1[,'NMD1'], xreg=xset, approximation = FALSE, allowmean = FALSE, allowdrift = FALSE)
summary(model1)
checkresiduals(model1)
fcast <- forecast(model1,xreg=xset, h=1)
print(summary(fcast))
autoplot(fcast)
My problems: -
While my model seems to work fine, I am not able to understand what value of h shall i put while forecasting. I also don't understand what frequency really is while we define a time series.
Please help.

Forecasting of multivariate data through Vector Autoregression model

I am working in the functional time series using the multivariate time series data(hourly time series data). I am using FAR model more than one order for which no statistical package is available in R, so for this I convert my data into functional form and obtained the functional principle component and from those FPCA I extract their corresponding** FPCscores**. Know I use the VAR model on those FPCscores for the forecasting of each 24 hours through the VAR model, but the VAR give me the forecasted value for all 23hours when I put phat=23, but whenever I put phat=24 for example want to predict each 24 hours its give the results in the form of NA. the code is given below
library(vars)
library(fda)
fdata<- function(mat){
nb = 27 # number of basis functions for the data
fbf = create.fourier.basis(rangeval=c(0,1), nbasis=nb) # basis for data
args=seq(0,1,length=24)
fdata1=Data2fd(args,y=t(mat),fbf) # functions generated from discretized y
return(fdata1)
}
prediction.ffpe = function(fdata1){
n = ncol(fdata1$coef)
D = nrow(fdata1$coef)
#center the data
#mu = mean.fd(fdata1)
data = center.fd(fdata1)
#ffpe = fFPE(fdata1, Pmax=10)
#p.hat = ffpe[2] #order of the model
d.hat=23
p.hat=6
#fPCA
fpca = pca.fd(data,nharm=D, centerfns=TRUE)
scores = fpca$scores[,0:d.hat]
# to avoid warnings from vars predict function below
colnames(scores) <- as.character(seq(1:d.hat))
VAR.pre= predict(VAR(scores, p.hat), n.ahead=1, type="const")$fcst
}
kindly guide me that how can I solve out my problem or what error I doing. THANKS

ARFIMA model and accurancy function

I am foresting with data sets from fpp2 package and forecast package. So my intention is to make automatic forecasting with a several time series. So for that reason I am forecasting with function. You can see code below:
# CODE
library(fpp2)
library(dplyr)
library(forecast)
df<-qauselec
# Forecasting function
fct_fun <- function(Z, hrz = forecast_horizon) {
timeseries <- msts(Z, start = 1956, seasonal.periods = 4)
forecast <- arfima(timeseries)
}
acc_list <- lapply(X = df, fct_fun)
So next step is to check accuracy of model. So for that reason I am trying with this line of code you can see below
accurancy_arfima <- lapply(acc_list, accuracy)
Until now this line of code or function accuracy worked perfectly with other models like snaive,ets etc. but with arfima can’t work properly.
So can anybody help me how to resolve this problem with accuracy function?

Follow R-documentation, Returns range of summary measures of the forecast accuracy. If x is provided, the function measures test set forecast accuracy based on x-f . If x is not provided, the function only produces training set accuracy measures of the forecasts based on f["x"]-fitted(f).
And usage summary can be seen :
accuracy(f, x, test = NULL, d = NULL, D = NULL,
...)
So :
accuracy(acc_list[[1]]$fitted, df)
If you want to evaluate separately accuracy, It will work.
a <- c()
for (i in 1:4) {
b <- accuracy(df[i], acc_list[[1]]$fitted[i])
a <- rbind(a,b)
}

arima model for multiple seasonalities in R

I'm learning to create a forecasting model for time series that has multiple seasonalities. Following is the subset of dataset that I'm refering to. This dataset includes hourly data points and I wish to include daily as well as weekly seasonalities in my arima model. Following is the subset of dataset:
data= c(4,4,1,2,6,21,105,257,291,172,72,10,35,42,77,72,133,192,122,59,29,25,24,5,7,3,3,0,7,15,91,230,284,147,67,53,54,55,63,73,114,154,137,57,27,31,25,11,4,4,4,2,7,18,68,218,251,131,71,43,55,62,63,80,120,144,107,42,27,11,10,16,8,10,7,1,4,3,12,17,58,59,68,76,91,95,89,115,107,107,41,40,25,18,14,15,6,12,2,4,1,6,9,14,43,67,67,94,100,129,126,122,132,118,68,26,19,12,9,5,4,2,5,1,3,16,89,233,304,174,53,55,53,52,59,92,117,214,139,73,37,28,15,11,8,1,2,5,4,22,103,258,317,163,58,29,37,46,54,62,95,197,152,58,32,30,17,9,8,1,3,1,3,16,109,245,302,156,53,34,47,46,54,65,102,155,116,51,30,24,17,10,7,4,8,0,11,0,2,225,282,141,4,87,44,60,52,74,135,157,113,57,44,26,29,17,8,7,4,4,2,10,57,125,182,100,33,27,41,39,35,50,69,92,66,30,11,10,11,9,6,5,10,4,1,7,9,17,24,21,29,28,48,38,30,21,26,25,35,10,9,4,4,4,3,5,4,4,4,3,5,10,16,28,47,63,40,49,28,22,18,27,18,10,5,8,7,3,2,2,4,1,4,19,59,167,235,130,57,45,46,42,40,49,64,96,54,27,17,18,15,7,6,2,3,1,2,21,88,187,253,130,77,47,49,48,53,77,109,147,109,45,41,35,16,13)
The code I'm trying to use is following:
tsdata = ts (data, frequency = 24)
aicvalstemp = NULL
aicvals= NULL
for (i in 1:5) {
for (j in 1:5) {
xreg1 = fourier(tsdata,i,24)
xreg2 = fourier(tsdata,j,168)
xregs = cbind(xreg1,xreg2)
armodel = auto.arima(bike_TS_west, xreg = xregs)
aicvalstemp = cbind(i,j,armodel$aic)
aicvals = rbind(aicvals,aicvalstemp)
}
}
The cbind command in the above command fails because the number of rows in xreg1 and xreg2 are different. I even tried using 1:length(data) argument in the fourier function but that also gave me an error. If someone can rectify the mistakes in the above code to produce a forecast of next 24 hours using an arima model with minimum AIC values, it would be really helpful. Also if you can include datasplitting in your code by creating training and testing data sets, it would be totally awesome. Thanks for your help.

I don't understand the desire to fit a weekly "season" to these data as there is no evidence for one in the data subset you provided. Also, you should really log-transform the data because they do not reflect a Gaussian process as is.
So, here's how you could fit models with a some form of hourly signals.
## the data are not normal, so log transform to meet assumption of Gaussian errors
ln_dat <- log(tsdata)
## number of hours to forecast
hrs_out <- 24
## max number of Fourier terms
max_F <- 5
## empty list for model fits
mod_res <- vector("list", max_F)
## fit models with increasing Fourier terms
for (i in 1:max_F) {
xreg <- fourier(ln_dat,i)
mod_res[[i]] <- auto.arima(tsdata, xreg = xreg)
}
## table of AIC results
aic_tbl <- data.frame(F=seq(max_F), AIC=sapply(mod_res, AIC))
## number of Fourier terms in best model
F_best <- which(aic_tbl$AIC==min(aic_tbl$AIC))
## forecast from best model
fore <- forecast(mod_res[[F_best]], xreg=fourierf(ln_dat,F_best,hrs_out))

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