auto.arima() is giving me no seasonal component for my series, even though I can see that there is one present. The function gives me a non seasonal ARIMA model of order (5,0,0). So, when I try to forecast using that model, it just gives the mean. The time series is of daily minimum temperatures in Melbourne, Australia for ten years.
Click this link to see the data and the auto.arima forecast
`
library(readr)
temp <- read_csv("~/Downloads/Melbourne Minimum Temp.csv",
col_types = cols(Date = col_date(format = "%m/%d/%y"),
Temp = col_number()))
t <- ts(temp$Temp, start = temp$Date\[1], end = temp$Date[nrow(temp)])
auto.arima(t, trace = T)
`
Tried using the data as a ts object, as an xts object, and as a vector.
Just reporting a good well explained - as usual - blogpost by Rob Hyndman.
https://robjhyndman.com/hyndsight/dailydata/
The relevant part to your question says (blockquoting exactly the page):
When the time series is long enough to take in more than a year, then
it may be necessary to allow for annual seasonality as well as weekly
seasonality. In that case, a multiple seasonal model such as TBATS is
required.
y <- msts(x, seasonal.periods=c(7,365.25))
fit <- tbats(y)
fc <- forecast(fit)
plot(fc)
This should capture the weekly pattern as well as the longer annual
pattern. The period 365.25 is the average length of a year allowing
for leap years. In some countries, alternative or additional year
lengths may be necessary.
I think it does exactly what you want.
I also tried to simply create the time series with msts
y <- msts(x[1:1800], seasonal.periods=c(7,365.25))
(I cut the time series in half to be quicker)
and then run auto.arima() directly on it, forcing a seasonal component with D=1
fc = auto.arima(y,D=1,trace=T,stepwise = F)
it will take a while.. because I set stepwise = FALSE (if you want it to look at all combinations without shortcuts you can set approximation=FALSE as well)
Series: y
ARIMA(1,0,3)(0,1,0)[365]
Coefficients:
ar1 ma1 ma2 ma3
0.9036 -0.3647 -0.3278 -0.0733
s.e. 0.0500 0.0571 0.0405 0.0310
sigma^2 estimated as 12.63: log likelihood=-3854.1
AIC=7718.19 AICc=7718.23 BIC=7744.54
and then the forecast
for_fc = forecast(fc)
plot(for_fc)
I am adding a figure with the complete time series (red) on top of the output of
plot(for_fc)
and it seems to work decently - but it was just a quick test.
Related
I am working with time series 551 of the monthly data of the M3 competition.
So, my data is :
library(forecast)
library(Mcomp)
# Time Series
# Subset the M3 data to contain the relevant series
ts.data<- subset(M3, 12)[[551]]
print(ts.data)
I want to implement time series cross-validation for the last 18 observations of the in-sample interval.
Some people would normally call this “forecast evaluation with a rolling origin” or something similar.
How can i achieve that ? Whats means the in-sample interval ? Which is the timeseries i must evaluate?
Im quite confused , any help in order to light up this would be welcome.
The tsCV function of the forecast package is a good place to start.
From its documentation,
tsCV(y, forecastfunction, h = 1, window = NULL, xreg = NULL, initial = 0, .
..)
Let ‘y’ contain the time series y[1:T]. Then ‘forecastfunction’ is
applied successively to the time series y[1:t], for t=1,...,T-h,
making predictions f[t+h]. The errors are given by e[t+h] =
y[t+h]-f[t+h].
That is first tsCV fit a model to the y[1] and then forecast y[1 + h], next fit a model to y[1:2] and forecast y[2 + h] and so on for T-h steps.
The tsCV function returns the forecast errors.
Applying this to the training data of the ts.data
# function to fit a model and forecast
fmodel <- function(x, h){
forecast(Arima(x, order=c(1,1,1), seasonal = c(0, 0, 2)), h=h)
}
# time-series CV
cv_errs <- tsCV(ts.data$x, fmodel, h = 1)
# RMSE of the time-series CV
sqrt(mean(cv_errs^2, na.rm=TRUE))
# [1] 778.7898
In your case, it maybe that you are supposed to
fit a model to ts.data$x and then forecast ts.data$xx[1]
fit mode the c(ts.data$x, ts.data$xx[1]) and forecast(ts.data$xx[2]),
so on.
What does this mean? My timeSeries has a frequency of 365, doesn't it? What I'm trying to do is make 3 years of daily forecasts, one day at a time. To put it differently, I'd like to get a forecast for the next day, 365*3 times.
library(forecast)
df = read.csv("./files/all_var_df.csv")
ts = as.timeSeries(df[, c(1, 2)])
train = as.timeSeries(ts[0:3285, ])
validation = ts[3285:4380]
fit_hw <- hw(train)
fit2_hw <- hw(validation, model=fit_hw)
onestep_hw <- fitted(fit2_hw)
Error in hw(train): The time series should
have frequency greater than 1.
Here is some info that might help you answer:
class(train)
> [1] "timeSeries"
head(train, 3)
> 2005-01-01 101634.4
> 2005-01-02 106812.5
> 2005-01-03 119502.8
length(train)
> [1] 3285
Without actually seeing your data I can only speculate. I can, however, recreate this problem using available datasets in R. In the library(fpp2) in R, the dataset ausair contains "Total annual air passengers (in millions) including domestic and international aircraft passengers of air carriers registered in Australia. 1970-2016."
Reading in this dataset as a ts (air <- window(ausair, start = 1990)), we get the following:
Time Series:
Start = 1990
End = 2016
Frequency = 1
[1] 17.55340 21.86010 23.88660 26.92930 26.88850 28.83140 30.07510 30.95350
[9] 30.18570 31.57970 32.57757 33.47740 39.02158 41.38643 41.59655 44.65732
[17] 46.95177 48.72884 51.48843 50.02697 60.64091 63.36031 66.35527 68.19795
[25] 68.12324 69.77935 72.59770
I will now use the hw() function to train with:
fc <- hw(air, seasonal = "additive")
This gives the following error:
Error in hw(air, seasonal = "additive") :
The time series should have frequency greater than 1.
What has happened here is that each datapoint corresponds to a whole year. So the Holt-Winters method is unable to find seasonality. The seasonal portion of the HW method follows the following equation:
Where the term represents the seasonality, and m the frequency. It doesn't make sense to talk about a repetitive seasonal pattern if there is only 1 data point in a time period.
The fix to your problem is in the way you define your time series object with ts(). One argument of the time series function is frequency. Without seeing your data I can't say what that value should be set to. Here is a site explaining the term frequency. It will be dependent on what seasonality your data exhibits. Does it repeat a seasonal pattern every week? Every quarter? If there is no seasonal pattern, you can switch to the function holt() which only uses an exponential decay term and trend term to find a pattern and will not give your error.
I have daily electric load data from 1-1-2007 till 31-12-2016. I use ts() function to load the data like so
ts_load <- ts(data, start = c(2007,1), end = c(2016,12),frequency = 365)
I want to remove the yearly and weekly seasonality from my data, to decompose the data and remove the seasonality, I use the following code
decompose_load = decompose(ts_load, "additive")
deseasonalized = ts_load - decompose_load$seasonal
My question is, am I doing it right? is this the right way to remove the yearly seasonality? and what is the right way to remove the weekly seasonality?
A few points:
a ts series must have regularly spaced points and the same number of points in each cycle. In the question a frequency of 365 is specified but some years, i.e. leap years, would have 366 points. In particular, if you want the frequency to be a year then you can't use daily or weekly data without adjustment since different years have different numbers of days and the number of weeks in a year is not integer.
decompose does not handle multiple seasonalities. If by weekly you mean remove the effect of Monday, of Tuesday, etc. and if by yearly you mean remove the effect of being 1st of the year, 2nd of the year, etc. then you are asking for multiple seasonalities.
end = c(2017, 12) means the 12th day of 2017 since frequency is 365.
The msts function in the forecast package can handle multiple and non-integer seasonalities.
Staying with base R, another approach is to approximate it by a linear model avoiding all the above problems (but ignoring correlations) and we will discuss that.
Assuming the data shown reproducibly in the Note at the end we define the day of week, dow, and day of year, doy, variables and regress on those with an intercept and trend and then construct just the intercept plus trend plus residuals in the last line of code to deseasonalize. This isn't absolutely necessary but we have used scale to remove the mean of trend in order that the three terms defining data.ds are mutually orthogonal -- Whether or not we do this the third term will be orthogonal to the other 2 by the properties of linear models.
trend <- scale(seq_along(d), TRUE, FALSE)
dow <- format(d, "%a")
doy <- format(d, "%j")
fm <- lm(data ~ trend + dow + doy)
data.ds <- coef(fm)[1] + coef(fm)[2] * trend + resid(fm)
Note
Test data used in reproducible form:
set.seed(123)
d <- seq(as.Date("2007-01-01"), as.Date("2016-12-31"), "day")
n <- length(d)
trend <- 1:n
seas_week <- rep(1:7, length = n)
seas_year <- rep(1:365, length = n)
noise <- rnorm(n)
data <- trend + seas_week + seas_year + noise
you can use the dsa function in the dsa package to adjust a daily time series. The advantage over the regression solution is, that it takes into account that the impact of the season can change over time, which is usually the case.
In order to use that function, your data should be in the xts format (from the xts package). Because in that case the leap year is not ignored.
The code will then look something like this:
install.packages(c("xts", "dsa"))
data = rnorm(365.25*10, 100, 1)
data_xts <- xts::xts(data, seq.Date(as.Date("2007-01-01"), by="days", length.out = length(data)))
sa = dsa::dsa(data_xts, fourier_number = 24)
# the fourier_number is used to model monthly recurring seasonal patterns in the regARIMA part
data_adjusted <- sa$output[,1]
I'm trying to decompose my data to see what the trend and seasonality effects are. I have 4 months of data, recorded daily. Data looks like:
date amount
11/1/2000 1700
11/2/2000 11087
11/3/2000 11248
11/4/2000 13336
11/5/2000 18815
11/6/2000 8820
11/7/2000 7687
11/8/2000 5514
11/9/2000 9591
11/10/2000 9676
11/11/2000 14782
11/12/2000 18554
And so forth to the end of Feb 2001. I read in the data like so and generate a timeseries object:
myvector <- read.table("clipboard", sep="\t", header=T)
myts <- ts(myvector$amount, start=c(2000,11), frequency=52)
I'm very confused as to how to read this data in as a time series object. The data is recorded daily, but if I use frequency=365, then try
fit <- stl(myts2, s.window="periodic")
I get:
Error in stl(myts2, s.window = "periodic") :
series is not periodic or has less than two periods
Every example I find does the object casting with multiple years worth of data. Is this not possible in my case?
I know the next steps for plotting the trend and decomposition are:
fit <- stl(myts, s.window="periodic")
plot(fit)
Try seasonal differencing, which is similar to regular differencing except is applied over different periods:
An example:
data(austres)
plot(austres)
seasonal <- diff(austres, lag = 12, differences = 1)
plot(seasonal)
d.seasonal <- diff(seasonal, differences = 2)
plot(d.seasonal)
Now you've made stationary the seasonal component of the time series.
I've been trying to develop an ARIMA model to forecast wind speed values. I have a four year data series (from january 2008 until december 2011). The series presents 10 minute data, which means that in a day we have 144 observations. Well, I'm using the first three years (observations 1 to 157157) to generate the model and the last year to validate the model.
The thing is I want to update the forecast. On other words, when one forecast ends up, more data is added to the dataset and another forecast is performed. But the result seems like I had just lagged the original series. Here's the code:
#1 - Load data:
z=read.csv('D:/Faculdade/Mestrado/Dissertação/velocidade/tudo_10m.csv', header=T, dec=".")
vel=ts(z, start=c(2008,1), frequency=52000)
# 5 - ARIMA Forecasts:
library(forecast)
n=157157
while(n<=157200){
amostra <- vel[1:n] # Only data until 2010
pred <- auto.arima(amostra, seasonal=TRUE,
ic="aicc", stepwise=FALSE, trace=TRUE,
approximation=TRUE, xreg=NULL,
test="adf",
allowdrift=TRUE, lambda=NULL, parallel=TRUE, num.cores=4)
velpred <- arima(pred) # Is this step really necessary?
velpred
predvel<- forecast(pred, h=12) # h means the forecast steps ahead
predvel
plot(amostra, xlim=c(157158, n), ylim=c(0,20), col="blue", main="Previsões e Observações", type="l", lty=1)
lines(fitted(predvel), xlim=c(157158, n), ylim=c(0,20), col="red", lty=2)
n=n+12
}
But when it plot the results (I couldn't post the picture here), it exhibits the observed series and the forecasted plot, which seems just the same as the observed series, but one step lagged.
Can anyone help me examining my code and/or giving tips on how to get the best of my model? Thanks! (Hope my English is understandable...)