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FM Time Series Plot

3.1 Modelling Reducing Balance Systems with Regular Repayments

Note: if you cannot remember what a reducing balance system is, revise notes for 1.2 Forms of Depreciation and 1.3 Predicting Future Values for Depreciation Systems.

Modelling using Recursion Relations

  • A reducing balance system with regular repayments describes a system which has a negative interest rate, and positive deposits made at the end of each compounding period.
  • We can use the simple recursion formula to model this system:

A_{n+1}=d+(1+I) A_{n}

Where d>0 and I<0.

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4.3 Numerical Smoothing using the Moving Median Method

Note: if you can’t remember the basics of numerical smoothing, revise notes for 4.2 Numerical Smoothing using the Moving Mean Method.

Moving Median Smoothing

  • The moving median smoothing method involves taking the median of each group.
  • This method is particularly effective when the exact values of data points are unknown (e.g. if the data is shown in a time series plot without the raw dataset).

Smooth a Single Point using an Odd Moving Median

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4.2 Numerical Smoothing using the Moving Mean Method

The Idea of Numerical Smoothing

  • Time series plots are often ‘noisy’, with many random fluctuations that make it difficult to analyse the long-term pattern of the data.
  • Numerical smoothing provides a method of lessening the impact of those random fluctuations so that the pattern is easier to discern.
  • The two methods for numerical smoothing used in further maths are moving mean and moving median smoothing.
  • In both methods, a new set of values are created by taking a group of data points, finding the mean or median, then moving to the next group (by replacing the first data point in the group with the next data point not yet included).
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4.1 Introduction to Time Series Plots

Time Series Plots

  • Time series plots are a specific type of graph, where the explanatory variable is time.
  • They are used to analyse how a system changes over time.
  • When describing a time series plot, the trend, seasonality, irregular fluctuations, structural change and outliers are all important aspects.
  • Time series plots can either be shown as a graph with data points connected by lines, or as a dot plot.
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