ARIMA

ARIMA stands for Autoregressive integrated moving average. These models are often known as Box–Jenkins method since they are named after the statisticians George Box and Gwilym Jenkins. ARIMA models find the best fit of a time-series model to past values of a time series.

Let's look at the ARIMA models

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Time Series with Trend

In a time series trend estimation can be used to express the long term increasing or decreasing tendencies that are statistically distinguishable from the random behavior of the system. A model can be used to describe such behavior of the observed data.

Linear time-series forecasting model is used when there is a trend in the underlying data which may be sufficiently represented by drawing a straight line and calculating its slope. Such a line must be drawn in a way that it “best fits” the data points of the scatter plot.

Many times a straight line is either misleading or insufficient; in such cases one may notice that parabola or a curve is a better fit instead of the straight line.

In some cases an exponential time series forecasting model is a better fit, specifically when the data series increases or decreases  at faster and faster rate as the values increase or decrease respectively.

In these set of slides we will take a look at estimating trends associated with time series data.

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Exponential Smoothing

This is a widely used and successful technique that is similar to weighted moving average. The intuition behind this technique is that one is relying upon “todays observed” and “yesterdays forecasted value of today” to calculate forecast for tomorrow. By nature this method ends up weighing recent observations more heavily that previous ones.

1. We will now take a look at the Exponential Smoothing of time series data

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Introduction

Time series analysis is the science that allows us to look at sequential data that is collected overtime and understand the randomness to define existing trends. An example use case will be to analyze market data and define a portfolio with known risk and expected returns.

Let us start with a simple introduction to Time Series:

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