Time Series

Author

LoweMackenzie

Published

October 20, 2024

Times Series Example

We will use this page to cover the example we did in class.

Libraries

First load these libraries. Remove hashtag before install.package to load library.

# Install the forecast package if not already installed
#install.packages("forecast")
# Load the package
library(forecast)
Warning: package 'forecast' was built under R version 4.3.3
Registered S3 method overwritten by 'quantmod':
  method            from
  as.zoo.data.frame zoo 
library(ggplot2)
Warning: package 'ggplot2' was built under R version 4.3.3

Data

And the following data Remember to switch the directory as this one is specific to my computer!

library(readxl)
croptimeseries<- read_excel("/Users/ashleylowe/Desktop/SpreadsheetModeling429/2025/In-class/croptimeseries.xlsx")

In - Class Example

Create Variable

  1. First make a variable that shows production by land used

    croptimeseries$production_byland=croptimeseries$`Production (million bushels)`/croptimeseries$`Planted area (million acres)`

    Exponential Smoothing

  2. Use the created variable to predict a exponential smoothing with a damping value of .9. (we will ignore .1 for this example)

Because R's ets() function is designed to automatically optimize and validate model parameters — and it will reject combinations (like AAN with phi = 0.1) that it determines are unstable or inappropriate for your data.

In contrast, Excel doesn’t optimize or reject your model. It simply applies the formula, even if it results in poor or unstable forecasts.

# Ensure your variable is a time series object
# Replace the frequency and start values as needed
ts_data <- ts(croptimeseries$production_byland, frequency = 1)

# Exponential smoothing with damping value = 0.9
model_damped_09 <- ets(ts_data, model = "AAN", damped = TRUE, phi = 0.9)
forecast_damped_09 <- forecast(model_damped_09)


# Get fitted values (same length as original data)
croptimeseries$fit_damped_09 <- as.numeric(fitted(model_damped_09))

Moving Average

  1. Create a moving average using the interval of a decade.

    Explanation

    • order = 10 — the window size (10 years)
# Apply 10-year (decade) moving average
croptimeseries$ma_10yr <- ma(ts_data, order = 10)

Line Graph

  1. Create a line graph that including your production by land (1), the exponential smoothing (2) and the moving average (3)
ggplot(croptimeseries, aes(x = Year)) +  # Make sure 'Year' exists and is correct
  geom_line(aes(y = production_byland, color = "Original"), size = 1) +
  geom_line(aes(y = fit_damped_09, color = "Exp. Smoothing (0.9)"), size = 1, linetype = "dashed") +
  geom_line(aes(y = ma_10yr, color = "10-Year Moving Average"), size = 1, linetype = "dotdash") +
  labs(title = "Production by Land with Exponential Smoothing and 10-Year Moving Average",
       x = "Year",
       y = "Production",
       color = "Legend") +
  theme_minimal()
Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
ℹ Please use `linewidth` instead.
Warning: Removed 10 rows containing missing values or values outside the scale range
(`geom_line()`).

MFE Calculation

mean( croptimeseries$production_byland- croptimeseries$fit_damped_09, na.rm = TRUE)
[1] 0.4943744
mean(croptimeseries$production_byland - croptimeseries$fit_damped_1 , na.rm = TRUE)
Warning: Unknown or uninitialised column: `fit_damped_1`.
[1] NaN
mean( croptimeseries$production_byland - croptimeseries$ma_10yr , na.rm = TRUE)
[1] 0.05435743