Time Series Forecasting with “Lynx Trappings” Dataset
R
# Load the packagelibrary(forecast)# Load the datasetdata(lynx)# Convert data to a time series objectts_data <- ts(lynx, frequency = 1, start = c(1821))# Fit an ARIMA model to the dataarima_model <- auto.arima(ts_data)# Split data into training and testing setstrain_data <- window(ts_data, start = c(1821), end = c(1900))test_data <- window(ts_data, start = c(1901))# Fit ARIMA model on training dataarima_model <- arima(train_data, order = arima_model$arma[c(1, 6, 2)])# Forecast using the ARIMA modelforecast_values <- forecast(arima_model, h = length(test_data))# Calculate RMSE to evaluate model performancermse <- sqrt(mean((forecast_values$mean - test_data)^2))print(paste("Root Mean Squared Error (RMSE):", round(rmse, 2)))# Plot the forecasted valuesplot(forecast_values, main = "Annual Lynx Trappings Forecast")lines(test_data, col = "blue") |
Output:
[1] "Root Mean Squared Error (RMSE): 1698.47"
Annual Lynx Trappings Forecast
- First loads the built-in “lynx” dataset into the R environment. This dataset contains the annual number of lynx trappings, which is often used for time series analysis.
- we convert the loaded data into a time series object using the ts() function. We specify the frequency as 1 since the data is annual, and we set the start year as 1821.
- auto.arima() function from the forecast package to automatically select an appropriate ARIMA model for the time series data. The function determines the order of differencing (d) and the orders of the autoregressive (p) and moving average (q) components.
- We split the time series data into two parts: a training set (from 1821 to 1900) and a testing set (from 1901 onwards). The training set is used to fit the ARIMA model, and the testing set is used to evaluate the model’s performance.
- ARIMA model to the training data using the order parameters determined by the auto.arima() function. The chosen order parameters are based on statistical criteria and are specified in the order argument
- We use the trained ARIMA model to make forecasts for the length of the testing set, which is the number of years from 1901 onwards. The forecast() function generates the forecasted values.
- We calculate the Root Mean Squared Error (RMSE) to evaluate the accuracy of the model’s forecasts. The RMSE measures the average error of the model’s predictions compared to the actual values in the testing set.
- Finally, we create a plot that displays the forecasted values along with the actual values from the testing set, allowing us to visually assess the model’s performance.
Machine Learning for Time Series Data in R
Machine learning (ML) is a subfield of artificial intelligence (AI) that focuses on the development of algorithms and models that enable computers to learn and make predictions or decisions without being explicitly programmed. In R Programming Language it’s a way for computers to learn from data and improve their performance on a specific task over time. Here are some key concepts in machine learning.
Time Series Data in R
Time series data is a sequence of observations or measurements collected or recorded at specific time intervals. This type of data is commonly found in various domains, including finance, economics, meteorology, and more. R provides several packages and functions to work with time series data effectively.
Time Series Components
Time series data is characterized by several key components that impact its behaviour and modelling. Understanding these components is crucial for accurate time series forecasting. The primary components are.
- Trend: The trend component represents the long-term movement or direction in the data. It reveals the overall pattern or behaviour over an extended period. Trends can be upward, downward, or relatively stable.
- Seasonality: Seasonality refers to periodic fluctuations or patterns that occur at regular intervals. These intervals could be daily, weekly, monthly, or yearly. For example, sales data often exhibits seasonality with higher sales during specific times of the year.
- Cyclic Patterns: Cyclic patterns are long-term wave-like movements that are not strictly periodic like seasonality. They typically have irregular durations and amplitudes. Identifying cyclic patterns can be challenging.
- Residuals: Residuals represent the random noise or irregular variations in the data that cannot be attributed to the trend, seasonality, or cyclic patterns. Accurate time series modelling involves minimizing these residuals.
Important steps required for Machine Learning for Time Series Data in R
Data: Machine learning algorithms require data to learn from. This data typically consists of features (input variables) and labels (output or target variables). For example, in image recognition, features might be pixel values, and labels would be the object classes.
Training: In the training phase, a machine learning model is presented with a dataset containing known inputs and outputs. The model learns to map inputs to outputs by adjusting its internal parameters.
Model: A machine learning model is a mathematical representation of a relationship between inputs and outputs. There are various types of ML models, including regression models, decision trees, neural networks, and more.
Learning: Learning refers to the process of adjusting the model’s parameters during training to minimize the difference between its predictions and the actual labels in the training data. This process is guided by a loss function that quantifies the model’s error.
Prediction: Once trained, a machine learning model can be used to make predictions or decisions on new, unseen data. It applies the learned patterns to new inputs to produce outputs or predictions.