In a study of 81 species of Australian plants Hudson & Keatley (2021) investigated whether the day of occurrence of a species first flowering (first flowering day, FFD, a number between 1 -365) is impacted by climate factors such as rainfall (rain), temperature (temp), radiation level (rad), and relative humidity (RH). The study by Hudson & Keatley essentially explores the influence of long-term climate on the FFD of 81 species of plants from 1984 to 2014.

Your data focuses on one species (of the 81) and contains 5 time series, the FFD time series of the given plant species and the contemporaneous yearly averaged climate variables measured from 1984 - 2014 (31 years). All series are available here in FFD .csv

Your task is to model FFD and forecast FFD. Single climate predictors (univariate models) are to be tested. Your task is to give best FFD 4 years ahead forecasts for the FFD series. Point forecasts and confidence intervals are required for the forecasts with appropriate graphs.

Provide the point forecasts and confidence intervals and corresponding plot for the most optimal model for each method used (DLM, ARDL, polyck, koyck, dynamic, exponential smoothing and state-space model).

Use MASE() function from the dLagM package to compute MASE for time series regression methods for model comparisons. Choice of optimal models within a specific method can be assessed from values of R squared, AIC, BIC, MASE etc (as is appropriate to the method).

Hints:

• Perform univariate analyse of predictors.
• Run models with and without intercept.
• Interpret the lag effects - note positive lag coefficient means that flowering is later and negative ones earlier flowering (lower FFD).
• Intercept denotes the intercept mean FFD. You are to analyse one given species (on Canvas).
• Plots are essential ACF PACF, forecasts etc.
• Percentiles method for relevant covariates for the forecasts can be used.