R r‑statistics.co

Time Series Exercises in R: 40 Practice Problems

Forty practice problems on time series in R: ts objects, decomposition, stationarity, autocorrelation, ARIMA, ETS, forecasting. Hidden solutions.

By Selva Prabhakaran  ·  Published May 11, 2026  ·  Last updated May 11, 2026
RRun this once before any exercise
library(forecast) library(tseries) library(dplyr) library(tibble)

  

  





Section 1. ts objects and basics (8 problems)



Exercise 1.1: Create a ts



Difficulty: Beginner. Monthly series starting Jan 2020.



Show solution



  

    
RInteractive R

    
ts(rnorm(24), frequency = 12, start = c(2020, 1))

    

      
      
    

    

  

  








Exercise 1.2: Plot ts



Difficulty: Beginner.



Show solution



  

    
RInteractive R

    
plot(AirPassengers)

    

      
      
    

    

  

  








Exercise 1.3: Frequency



Difficulty: Beginner.



Show solution



  

    
RInteractive R

    
frequency(AirPassengers)

    

      
      
    

    

  

  








Exercise 1.4: Window subset



Difficulty: Intermediate.



Show solution



  

    
RInteractive R

    
window(AirPassengers, start = c(1955,1), end = c(1957,12))

    

      
      
    

    

  

  








Exercise 1.5: Aggregate to yearly



Difficulty: Intermediate.



Show solution



  

    
RInteractive R

    
aggregate(AirPassengers, FUN = sum)

    

      
      
    

    

  

  








Exercise 1.6: Lag



Difficulty: Intermediate.



Show solution



  

    
RInteractive R

    
lag(AirPassengers, k = -1)

    

      
      
    

    

  

  








Exercise 1.7: Difference



Difficulty: Intermediate.



Show solution



  

    
RInteractive R

    
diff(AirPassengers)

    

      
      
    

    

  

  








Exercise 1.8: Seasonal lag-12 difference



Difficulty: Advanced.



Show solution



  

    
RInteractive R

    
diff(AirPassengers, lag = 12)

    

      
      
    

    

  

  








Section 2. Decomposition (6 problems)



Exercise 2.1: Classical decomposition



Difficulty: Intermediate.



Show solution



  

    
RInteractive R

    
plot(decompose(AirPassengers))

    

      
      
    

    

  

  








Exercise 2.2: Multiplicative decomposition



Difficulty: Intermediate.



Show solution



  

    
RInteractive R

    
plot(decompose(AirPassengers, type = "multiplicative"))

    

      
      
    

    

  

  








Exercise 2.3: STL decomposition



Difficulty: Advanced.



Show solution



  

    
RInteractive R

    
plot(stl(AirPassengers, s.window = "periodic"))

    

      
      
    

    

  

  








Exercise 2.4: Extract trend



Difficulty: Advanced.



Show solution



  

    
RInteractive R

    
decompose(AirPassengers)$trend

    

      
      
    

    

  

  








Exercise 2.5: Seasonally adjusted



Difficulty: Advanced.



Show solution



  

    
RInteractive R

    
d <- decompose(AirPassengers)
AirPassengers - d$seasonal

    

      
      
    

    

  

  








Exercise 2.6: Strength of seasonality



Difficulty: Advanced.



Show solution



  

    
RInteractive R

    
mstl(AirPassengers) |> head()

    

      
      
    

    

  

  








Section 3. Stationarity and autocorrelation (6 problems)



Exercise 3.1: ACF plot



Difficulty: Beginner.



Show solution



  

    
RInteractive R

    
acf(AirPassengers)

    

      
      
    

    

  

  








Exercise 3.2: PACF plot



Difficulty: Intermediate.



Show solution



  

    
RInteractive R

    
pacf(AirPassengers)

    

      
      
    

    

  

  








Exercise 3.3: ADF test for stationarity



Difficulty: Intermediate.



Show solution



  

    
RInteractive R

    
adf.test(AirPassengers)

    

      
      
    

    

  

  








Exercise 3.4: KPSS test



Difficulty: Intermediate.



Show solution



  

    
RInteractive R

    
kpss.test(AirPassengers)

    

      
      
    

    

  

  








Exercise 3.5: Difference until stationary



Difficulty: Advanced.



Show solution



  

    
RInteractive R

    
ndiffs(AirPassengers)

    

      
      
    

    

  

  








Exercise 3.6: Seasonal differences needed



Difficulty: Advanced.



Show solution



  

    
RInteractive R

    
nsdiffs(AirPassengers)

    

      
      
    

    

  

  








Section 4. ARIMA (8 problems)



Exercise 4.1: Auto ARIMA



Difficulty: Intermediate.



Show solution



  

    
RInteractive R

    
fit <- auto.arima(AirPassengers)
fit

    

      
      
    

    

  

  








Exercise 4.2: Specific ARIMA(p,d,q)



Difficulty: Intermediate.



Show solution



  

    
RInteractive R

    
arima(AirPassengers, order = c(1, 1, 1))

    

      
      
    

    

  

  








Exercise 4.3: Seasonal ARIMA



Difficulty: Advanced.



Show solution



  

    
RInteractive R

    
arima(AirPassengers, order = c(1,1,1), seasonal = c(1,1,1))

    

      
      
    

    

  

  








Exercise 4.4: Forecast horizon



Difficulty: Intermediate.



Show solution



  

    
RInteractive R

    
fit <- auto.arima(AirPassengers)
forecast(fit, h = 24)

    

      
      
    

    

  

  








Exercise 4.5: Plot forecast



Difficulty: Intermediate.



Show solution



  

    
RInteractive R

    
fit <- auto.arima(AirPassengers)
plot(forecast(fit, h = 24))

    

      
      
    

    

  

  








Exercise 4.6: Residual diagnostics



Difficulty: Advanced.



Show solution



  

    
RInteractive R

    
fit <- auto.arima(AirPassengers)
checkresiduals(fit)

    

      
      
    

    

  

  








Exercise 4.7: Ljung-Box test



Difficulty: Advanced.



Show solution



  

    
RInteractive R

    
fit <- auto.arima(AirPassengers)
Box.test(residuals(fit), lag = 12, type = "Ljung-Box")

    

      
      
    

    

  

  








Exercise 4.8: AIC comparison



Difficulty: Advanced.



Show solution



  

    
RInteractive R

    
f1 <- arima(AirPassengers, order = c(1,1,1))
f2 <- arima(AirPassengers, order = c(2,1,2))
c(AIC(f1), AIC(f2))

    

      
      
    

    

  

  








Section 5. ETS and others (6 problems)



Exercise 5.1: Auto ETS



Difficulty: Intermediate.



Show solution



  

    
RInteractive R

    
ets(AirPassengers)

    

      
      
    

    

  

  








Exercise 5.2: Specific ETS



Difficulty: Advanced. Holt-Winters multiplicative.



Show solution



  

    
RInteractive R

    
ets(AirPassengers, model = "MAM")

    

      
      
    

    

  

  








Exercise 5.3: Holt-Winters



Difficulty: Intermediate.



Show solution



  

    
RInteractive R

    
HoltWinters(AirPassengers)

    

      
      
    

    

  

  








Exercise 5.4: Naive forecast



Difficulty: Beginner.



Show solution



  

    
RInteractive R

    
naive(AirPassengers, h = 12) |> autoplot()

    

      
      
    

    

  

  








Exercise 5.5: Seasonal naive



Difficulty: Beginner.



Show solution



  

    
RInteractive R

    
snaive(AirPassengers, h = 12)

    

      
      
    

    

  

  








Exercise 5.6: Mean forecast



Difficulty: Beginner.



Show solution



  

    
RInteractive R

    
meanf(AirPassengers, h = 12)

    

      
      
    

    

  

  








Section 6. Train-test and accuracy (6 problems)



Exercise 6.1: Train-test split



Difficulty: Intermediate.



Show solution



  

    
RInteractive R

    
train <- window(AirPassengers, end = c(1958, 12))
test  <- window(AirPassengers, start = c(1959, 1))
list(train = length(train), test = length(test))

    

      
      
    

    

  

  








Exercise 6.2: Forecast accuracy



Difficulty: Intermediate.



Show solution



  

    
RInteractive R

    
train <- window(AirPassengers, end = c(1958, 12))
test  <- window(AirPassengers, start = c(1959, 1))
fit <- auto.arima(train)
fc  <- forecast(fit, h = length(test))
accuracy(fc, test)

    

      
      
    

    

  

  








Exercise 6.3: Compare ARIMA vs ETS



Difficulty: Advanced.



Show solution



  

    
RInteractive R

    
train <- window(AirPassengers, end = c(1958, 12))
test  <- window(AirPassengers, start = c(1959, 1))
f1 <- forecast(auto.arima(train), h = length(test))
f2 <- forecast(ets(train), h = length(test))
list(arima = accuracy(f1, test)[2,"RMSE"],
     ets   = accuracy(f2, test)[2,"RMSE"])

    

      
      
    

    

  

  








Exercise 6.4: Cross-validation rolling origin



Difficulty: Advanced.



Show solution



  

    
RInteractive R

    
e <- tsCV(AirPassengers, forecastfunction = function(x, h) forecast(auto.arima(x), h = h), h = 1)
sqrt(mean(e^2, na.rm = TRUE))

    

      
      
    

    

  

  








Exercise 6.5: MAPE



Difficulty: Intermediate.



Show solution



  

    
RInteractive R

    
train <- window(AirPassengers, end = c(1958, 12))
test  <- window(AirPassengers, start = c(1959, 1))
fc <- forecast(auto.arima(train), h = length(test))
accuracy(fc, test)[, "MAPE"]

    

      
      
    

    

  

  








Exercise 6.6: Out-of-sample forecast plot



Difficulty: Intermediate.



Show solution



  

    
RInteractive R

    
fit <- auto.arima(AirPassengers)
autoplot(forecast(fit, h = 36))

    

      
      
    

    

  

  








What to do next



    


  • ARIMA-Exercises (coming), focused ARIMA drilling.
    • 


  • Linear-Regression-Exercises (shipped), regression on time-features.
    • 





        


        
      


      

        

        
© 2016-2026 Selva Prabhakaran.
          This work is licensed under the Creative Commons License.
        

        

          About ·
          RSS