Nicholas Masagao

# Time series Analysis

Time series analysis is a statistical technique that deals with the analysis of data collected at regular intervals over time. It is used to study the behavior of a variable over time and to make predictions about future values of the variable based on past values.

In time series analysis, the variable of interest is plotted against time on a graph, called a time series plot. The plot shows the pattern of the variable over time, which can be used to identify trends, seasonality, and other patterns in the data.

The main objective of time series analysis is to model the underlying structure of the time series and to make forecasts about future values of the variable. There are two main approaches to time series analysis: the time domain approach and the frequency domain approach.

In the time domain approach, the time series data is analyzed in its original form, without any transformation. This approa

ch involves fitting a mathematical model to the data and using the model to make forecasts about future values of the variable.

The frequency domain approach involves transforming the time series data into its frequency components, using techniques such as Fourier analysis. This approach is useful for identifying patterns in the data that may not be visible in the time domain.

Some of the commonly used techniques in time series analysis include:

Moving average: This technique involves taking the average of a certain number of past values of the variable to smooth out short-term fluctuations and identify long-term trends.

Exponential smoothing: This technique involves giving more weight to recent values of the variable than to past values, to capture the trend and seasonality of the data.

Autoregressive Integrated Moving Average (ARIMA) modeling: This technique involves modeling the time series data as a combination of autoregressive, moving average, and differencing terms, to capture the underlying structure of the data.

Seasonal decomposition: This technique involves separating the time series data into its trend, seasonality, and residual components, to identify the patterns in each component.

Time series analysis has applications in various fields, including economics, finance, engineering, and environmental sciences. It is useful for predicting future values of a variable, detecting anomalies, and identifying patterns in the data.

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