# Which of the following is additive model of time series

## Introduction

An additive model of a time series is one where the value of the time series at each time point is a sum of the values of all the previous time points plus some additional noise. This is in contrast to a multiplicative model, where the value at each time point is a product of the values of all the previous time points, plus some additional noise.

Additive models are generally easier to work with and are more commonly used in time series analysis. They are also more robust to outliers since an outlier at one-time point will not have as much impact on subsequent values as it would in a multiplicative model.

## What is an additive model?

An additive model is a time series model in which the individual terms are added together. This model is often used to predict future time series values, such as sales figures or economic indicators. Additive models are usually easier to interpret and faster to compute than other types of time series models, such as multiplicative models.

## Additive models of time series

A time series can be expressed as the sum of two components: a trend and a seasonality. In an additive model, these two components are added together to produce the final result. This type of model is generally used when the data points in the time series are evenly spaced in time.

## Why use an additive model?

There are several reasons why you might want to use an additive model:
-If your data are stationary (i.e. the mean and variance do not change over time), then an additive model is appropriate.
-If your data are not homogeneous (i.e. they vary in level or trend over time), then an additive model is appropriate.
-If you want to make forecasts for individual time series, then an additive model is appropriate.
-If you want to add or remove seasonal components from your data, then an additive model is appropriate.

## How to build an additive model

An additive model is one where the effect of each independent variable is simply added to the outcome. This contrasts with a multiplicative model, where the effect of each independent variable is multiplied by the outcome.

There are two common ways to build an additive model:

1. The first way is to identify the independent variables that are most likely to have an effect on the outcome, and then to add them one at a time to see if they improve the predictive power of the model.
2. The second way is to use all of the independent variables in the model at once, and then to select those that have the most predictive power.

Once you have selected the best predictor variables for your additive model, you can then use them to make predictions about future outcomes.

## Conclusion

The additive model of time series states that the time series is a linear combination of three components: the level, the trend, and the seasonality. The level is the mean of the series, the trend is the long-term change in the series, and the seasonality is the short-term fluctuations in the series.