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]
Related
I am looking into ambient air pollution within regions of NSW and conducting a daily time series decomposition analysis using Rbeast to investigate if there is a change point signature around the time of Covid-19 lockdowns.
I have created a looping code to analyse the data for each pollutant within each region - however the Beast X axis ("Date" - i.e. 01-01-2021 - ideally would plot years (2012-2022) is plotting strangely ( I.e. Time = 16000, 17000, 18000 etc.?).
Anyone know how to fix this?
beast_output = list()
target_pollutants = c("PM10", "OZONE", "NO", "NO2")
target_sites = c("WOLLONGONG", "MUSWELLBROOK", "SINGLETON", "CAMBERWELL", "WAGGAWAGGANORTH", "RICHMOND", "CAMDEN", "CHULLORA", "EARLWOOD", "WALLSEND", "BERESFIELD", "BARGO", "BRINGELLY", "PROSPECT", "STMARYS", "OAKDALE", "RANDWICK", "ROZELLE", "NEWCASTLE", "KEMBLAGRANGE", "ALBIONPARKSOUTH")
for (poll in target_pollutants) {
beast_output[[poll]] = list()
df = time_by_poll[[poll]] # grab the target df
sites = colnames(df)
sites$Date = NULL # clear date from the list
for (site in sites) {
ts = ts(df[[site]], start=min(df$Date), end=max(df$Date))
beast_results = beast(ts)
# plot(beastie_resulty)
beast_output[[poll]][[site]] = beast_results
}
}
plot (beast_results[["OZONE"]][["RANDWICK"]])
Thanks for asking and sorry about the issue. Indeed, the API interface in Rbeast is kinda confusing because it was originally coded to handle satellite time series.
Regardless, the BEAST model in the package was formulated only for regular time series.(By regular, I mean equally-spaced time series with the same number of data points per period.) Because leap years have 366 days but others have 356 days, daily time series are treated in BEAST as irregular time series if the periodicity is one year. However, if the periodic variation is weekly/7 days, daily time series are considered as regular. In order to handle irregular time series, I implemented the beast.irreg function which accepts irregular inputs and aggregate them into regular time series before doing the decomposition and changepoint detection.
To illustrate, I got a sample PM10 dataset for several regions (e.g., WOLLONGONG", and "MUSWELLBROOK") from this site https://www.dpie.nsw.gov.au/air-quality/air-quality-data-services/data-download-facility, and I posted the CSV file (as well as another dataset on ozone) under https://github.com/zhaokg/Rbeast/tree/master/R/SampleData. You can directly read the files from R as shown below:
df = read.csv('https://github.com/zhaokg/Rbeast/raw/master/R/SampleData/pm10_1658112168.csv',header=FALSE,skip=3)
dates = as.Date(df[,1], "%d/%m/%Y") # the 1st col is dates
Y = df[,2:ncol(df)] # the rest are PM10 data for the several sample sites
# e.g., Y[,1] for the first region (WOLLONGONG)
library(Rbeast)
o = beast.irreg(log(Y[,1]),time=dates,deltat=1/12, freq=12, tseg.min=3, sseg.min=6)
# log(Y[,1]) : Log-transformation may help if data is skewed bcz the BEAST model
assumes Gaussian errors;
# time=dates : Use the 'time' arg to supply the times of individual data points.
Alternatively, the `beast123' function also handles date strings of different formats
# deltat=1/12: Aggregate the daily time series into a regular one at the interval
of 1 month=1/12 year
# freq=12 : The period is 1 year, which is 12 data points (1.0/deltat=12)
# tseg.min: The minimum trend segment length allowed in the changepoint detection is 3 data points (3 months)
-- the results MAY be sensitive to this parameter
# sseg.min: The minimum seasonal segment length allowed in the changepoint detection is 6 data points (6 months)
-- the results MAY be sensitive to this parameter
plot(o)
# For sure, the daily time series can be re-sampled/aggregated to a different time interval
# Below, it is aggregated into a half monthly time series (dT=1/24 year), and the number
# of data points per period is freq=1.0 year/dT=24
o = beast.irreg( log(Y[,1]),time=dates, deltat = 1/24, freq=24, tseg.min=12, sseg.min=12)
plot(o)
# Aggregated to a weekly time series (e.g., dT=7 / 365 year: the unit again is year),
# and freq=1 year/ dT = 365/7.
# tcp.minmax=c(0,10) : the min and max numbers of changepoints allowed in the trend component
o = beast.irreg( log(Y[,1]),time=dates,deltat=7/365,freq=365/7, tcp.minmax=c(0,15),tseg.min=5, sseg.min=20,ocp=10)
plot(o)
# Finally if you want to run on the daily interval. Specify the dT=deltat=1/365 year, and
# freq = period/dT= 1.0 year/(1/365)year =365. Bcz the raw data is daily,
# the majority of the raw data is kept intact during the aggregation except when
# there is a leap year (the last two days of the leap year are merged into a single day)
o = beast.irreg( log(Y[,1]),time=dates, deltat = 1/365, freq=365/1, tseg.min=30, sseg.min=180)
plot(o)
By default, a time series is decomposed as Y= season + trend + error, but for your dataset in the original scale (e.g., not log-tranformed), there could be some spikes. One way to model this is to add an extra spike/outlier component: Y=season+trend+outlier/spike-like+error
# Use 'ocp' to specify the maximum number of spikes (either upward or downward) to be allowed in the outlier/spike component
o = beast.irreg(Y[,1],time=dates, deltat = 1/365, freq=365/1, tseg.min=30, sseg.min=180, ocp=10)
plot(o)
Below is an example for one time series analyzed at the weekly interval (Again, the exact results vary, depending on the choices of tseg.min or sseg.min).
More important, another issue I noticed from your figure is that your data seem to have lots of missing values, which should be assigned NA but instead assigned zeros in your figure. If that is the case, the analysis result for certain would be wrong. BEAST can handle missing data and these missing values should be given NA or NAN (e.g., Y[Y==0]=NA).
I am looking to forecast my time series. I have the following period daily data 2021-Jan-1 to 2022-Jul-1.
So I have a column of observations for each day.
what I tried so far:
d1=zoo(data, seq(from = as.Date("2021-01-01"), to = as.Date("2022-07-01"), by = 1))
tsdata <- ts(d1, frequency = 365)
ddata <- decompose(tsdata, "multiplicative")
I get following error here:
Error in decompose(tsdata, "multiplicative") :
time series has no or less than 2 periods
From what i have read it seems like because I do not have two full years? is that correct? I have tried doing it weekly as well:
series <- ts(data, frequency = 52, start = c(2021, 1))
getting the same issue.
How do I go about it without having to extend my dataset to two years since I do not have that, and still being able to decompose it?
Plus when I am actually trying to forecast it, it isn't giving me good enough forecast:
Plot with forecast
My data somewhat resembles a bell curve during that period. so is there a better fitting timeseries model I can apply instead?
A weekly frequency for daily data should have frequency = 7, not 52. It's possible that this fix to your code will produce a model with a seasonal term.
I don't think you'll be able to produce a time series model with annual seasonality with less than 2 years of data.
You can either produce a model with only weekly seasonality (I expect this is what most folks would recommend), or if you truly believe in the annual seasonal pattern exhibited in your data, your "forecast" can be a seasonal naive forecast that is simply last year's value for that particular day. I wouldn't recommend this, because it just seems risky, and I don't really see the same trajectory in your screenshot over 2022 that's apparent in 2021.
decompose requires two full cycles and that a full cycle represent 1 time unit. ts class can't use Date class anyways. To use frequency 7 we must use times 1/7th apart such as 1, 1+1/7, 1+2/7, etc. so that 1 cycle (7 days) covers 1 unit. Then just label the plot appropriately rather than using those times on the X axis. In the code below use %Y in place of %y if the years start in 19?? and end in 20?? so that tapply maintains the order.
# test data
set.seed(123)
s <- seq(from = as.Date("2021-01-01"), to = as.Date("2022-07-01"), by = 1)
data <- rnorm(length(s))
tsdata <- ts(data, freq = 7)
ddata <- decompose(tsdata, "multiplicative")
plot(ddata, xaxt = "n")
m <- tapply(time(tsdata), format(s, "%y/%m"), head, 1)
axis(1, m, names(m))
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.
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 have a data with two different monthly series and a one year overlap
ts1 <- ts(cumsum(rnorm(120,.1,1)), start = 1995, frequency = 12)
ts2 <- ts(cumsum(rnorm(120,.2,1)), start = 2004, frequency = 12)
They do not have the same levels (there was a rebasing in 2004) but with the overlap one can use the monthly growth rate of the first one to back-project the second one until 1995.
I would like to create a variable ts_series which has the levels of ts2 after 2004 and then uses the monthly growth rates of ts1 to back-project it. I have several such series in a zoo object, so I can either use a zoo method or group them in list and use mapply.
Many thanks
Here is one approach, using a simple linear regression on the overlapping bits to identify the relationship between the two series and then applying that model to the non-overlapping part of ts1 to estimate earlier values of ts2. The last step gives you a new ts object that represents the predicted values of ts2 for the non-overlapping period.
# Make the toy data
set.seed(1)
ts1 <- ts(cumsum(rnorm(120,.1,1)), start = 1995, frequency = 12)
ts2 <- ts(cumsum(rnorm(120,.2,1)), start = 2004, frequency = 12)
# Now do the estimation
x <- as.vector(window(ts1, start = c(2004,1), end = c(2004,12)))
y <- as.vector(window(ts2, start = c(2004,1), end = c(2004,12)))
tsmod <- lm(y ~ x)
ts2preds <- predict(tsmod, newdata = as.data.frame(window(ts1, start = c(1995,1), end = c(2003,12))))
ts2prior <- ts(data = ts2preds, start = c(1995, 1), end = c(2003, 12), frequency = 12)
If you want instead to backcast ts2 on its own, though, Rob Hyndman's got you covered with the forecast() function in his forecast package. Following an example from his blog:
library(forecast)
f <- frequency(ts2) # Identify the frequency of your ts
h <- (start(ts2)[1] - start(ts1)[1]) * f # Set the number of periods you want to backcast
revx <- ts(rev(ts2), frequency = f) # Reverse time in the series you want to backcast
ts2plus <- forecast(auto.arima(revx), h) # Do the backcasting
# Reverse its elements
ts2plus$mean <- ts(rev(ts2plus$mean), end=tsp(ts2)[1] - 1/f, frequency=f)
ts2plus$upper <- ts2plus$upper[h:1,]
ts2plus$lower <- ts2plus$lower[h:1,]
ts2plus$x <- ts2 # Replace the reversed reference series in the prediction object with the original one
# Plot it
plot(ts2plus, xlim=c(tsp(ts2)[1]-h/f, tsp(ts2)[2]))
Here's the plot that produces:
And here's how the two series compare:
> cor(ts2plus$mean, ts2preds)
[1] 0.9760174
If your main goal is to get the best possible point predictions of those earlier values, you might consider running both versions and averaging their results. Then this becomes a very simple multi-model ensemble forecast (or backcast).