# Time Series

## What is Time Series Data

Time series data is a sequence of data values that are collected over different intervals of time. The data is present in chronological order of time, allowing us to track changes over time.

## What is Time Series Analysis

Time series analysis is the analysis of a sequence of data points collected over an interval of time. It deals with analysing how the same information collected at different times varies.

The main assumption of time series analysis is that the past behaviour of data will be repeated.

`The whole time series analysis is based on the assumption that the data under consideration is stationary.`

## Properties of Time Series

Below are a few properties of time series data:

• Data is present in chronological order of time.
• There is no limit to the time range. It can be a day, month or century etc.
• The time period is the time between the start and end value.
• Graphs don’t follow any of the standard distributions you may have learnt in statistics and probability.
• Frequency is how often the data is recorded i.e daily, monthly, or annually.
• Time series data doesn’t follow Gaus Markov’s Assumption.
• It assumes that the patterns in the variable will continue in the future.

## Key Concepts of Time Series

There are four key concepts of time series: trend, seasonality, cyclic and stationarity.

### 1. Trend

The trend is the movement of time series to a higher or lower value over a long period of time. The trend may be an uptrend,Â downtrend or sideways trend.

### 2. Seasonality

A time series data is said to be seasonal if specific patterns appear on a cyclical basis. Seasonality can be of two types: additive and multiplicative.

#### a. Additive Seasonality

In additive seasonality, the magnitude of seasonal fluctuation is constant.

#### b. Multiplicative Seasonality

In multiplicative seasonality, the magnitude of seasonal fluctuation is not constant.

### 3. Cyclic

A time series data with rise and fall components without fixed frequency is regarded as cyclical.

```Differentiating seasonal and cyclic data can be a bit difficult. In seasonality,the same behaviour or pattern is seen
over time i.e the components rise and fall with a fixed frequency whereas cyclicity in a time series data is present
due to economical or business conditions and the frequency of rise and fall of the components is not fixed.```

### 4. Stationary

A time series data is said to be stationary if its properties like mean and standard deviation don’t change with time and there is no trend or seasonality in the data.

## Autocorrelation

Autocorrelation is the correlation between a variable with its previous values.

## White Noise

White Noise is a sequence of random numbers where every value has a time associated with it but the data doesn’t follow any pattern. It has a constant mean, standard deviation and no autocorrelation. Therefore white noise data is stationary.

Since white noise data doesn’t follow any pattern, we cannot predict the future value.

## Random Walk

Random walk is a special type of time series data in which it seems like values persist over time but the difference between different periods is simply white noise.

## Applications of Time Series

Time Series Data is used in various domains for analysis and predictions. Below are a few areas where time series analysis can be useful:

1. Stock Prices Forecasting
2. Interest Rates Prediction
3. Weather Forecasting
4. Sales Forecasting

## Limitations of Time Series Analysis

1. Time series analysis mostly works on a single feature.
2. Data needs to be transformed.
3. A bit expensive compared to normal data analysis.