Comprehensive Guide to Time Series Analysis in Actuarial Science

What is Time Series?

A time series is a sequence of observations recorded at different time intervals. Unlike cross-sectional data, where observations are independent, time series data points are dependent on one another. The time aspect is critical because the value at any time period can be influenced by previous values, seasonal factors, or even long-term trends.

Example: Yearly insurance claims or monthly lapse rates for life insurance policies are typical time series datasets in actuarial science.

Key Components of Time Series

1. Trend: The long-term direction of the data over time, either upward, downward, or constant.

   • Example: An increase in life insurance premiums collected over several years.

2. Seasonality: Regular, repeating patterns in data that occur at fixed intervals (daily, monthly, yearly).

   • Example: A spike in health insurance claims during flu season.

3. Cyclic Patterns: Long-term oscillations in data that occur without fixed intervals. These cycles last for longer periods than seasonal fluctuations.

   • Example: Economic cycles that affect insurance policy renewals.

4. Random or Irregular Variation: Unpredictable, non-repeating deviations caused by random events.

   • Example: Sudden spikes in claims due to a natural disaster.

Applications of Time Series in Actuarial Science

1. Mortality Forecasting:

   • Actuaries use time series models to predict future mortality rates. This is essential for determining premium pricing, reserving for life insurance, and pension planning. Models like Lee-Carter are widely used for mortality projections, where trends and stochastic time series approaches are combined to project future mortality improvements.

2. Insurance Claims:

   • Time series analysis helps in forecasting claim amounts. For instance, using ARIMA models, actuaries can predict next year’s claims based on historical claims data, adjusted for inflation and seasonality.

3. Lapse Rates:

   • In life insurance, policy lapse rates tend to fluctuate over time. Time series analysis helps understand the factors driving lapses (e.g., economic downturns, policyholder behavior) and allows actuaries to predict future lapse rates.

4. Premium Forecasting:

   • Predicting the future premiums an insurance company will collect is vital for financial planning. By analyzing past premiums with time series methods, actuaries can provide estimates for future cash inflows, adjusted for potential fluctuations.

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Practical Example: Forecasting Life Insurance in New York

Let’s apply time series analysis to life insurance data from New York.

Data: The dataset contains information on life insurance policies in force in New York from 1996 onwards.

Data Source: Life Insurance In Force in the State of New York: Beginning 1996 - Catalog (data.gov)

Steps:

1. Read the data: The data was imported and cleaned using readr in R.

2. Convert to Time Series: We transformed the life insurance data into a time series object using the ts() function in R.

3. ARIMA Modeling: Using auto.arima(), we identified the best-fitting ARIMA model for the dataset.

4. Forecasting: The ARIMA model was used to forecast the number of life insurance policies in force for the next 5 years.

5. Visualization

R Code

Read CSV file and Sorting the Data

Plotting the data - line and bar chart

Forecasting the data using time series

Visualization

Outputs :