Time Series Analysis and its components
Introduction to Time series
A time series is a collection of data points that appear in a logical sequence over a period of time. Cross-sectional data, on the other hand, captures a single moment in time. A time series is a set of data that follows the progression of a sample over time. A time series, allows you to see what causes influence certain variables from one period to the next. Time series analysis is important for determining how an asset, security, or economic variable change over time.
In both fundamental and technical analysis, time series forecasting methods are applied. Despite the fact that cross-sectional data is considered the polar opposite of time series data, the two are frequently utilized together in practice.
Time series data can be classified into two types:
1) Measurements gathered at regular time intervals (metrics)
2) Measurements gathered at irregular time intervals (events)
A time series is a set of data that follows the progression of a sample over time. A time series, allows you to see what causes influence certain variables from one period to the next. Time series analysis is important for determining how an asset, security, or economic variable changes over time. For instance,
· Time series analysis is used to forecast future values based on existing data.
· Time series analysis is a technique for detecting fluctuations in economics and business.
· It facilitates the assessment of current accomplishments.
· Pattern identification, weather forecasting, signal processing, and earthquake prediction all require time series.
· Time series analysis is a powerful instrument in the hands of corporate leaders when it comes to planning sales, prices, policies, and production.
Stationary and Markov Property
Stationary Property
The qualities of a stationary statistic are independent of the time at which the series is observed. As a result, statistics with trends or seasonality aren’t stationary; the trend and seasonality will impact the statistic’s value at different times. A noise series, on the other hand, is stationary — it doesn’t matter when you look at it; it should seem the same at any point in time.
A statistic with cyclic behavior (but no trend or seasonality) is called stationary in some instances. This could be because the cycles don’t appear to be of a fixed length, thus we can’t be sure where the peaks and troughs of the cycles are until we examine the series.
Markov Property
The Markov property is a prevalent assumption in economic and financial modeling, and it may be a fundamental property in statistical analysis. The conditional characteristic function is embedded in a high-frequency domain approach, and it is used to build a test for the Markov property that verifies the implication of the Markov property in every conditional instant (if any) and over many lags.
The suggested test works for univariate and multivariate statistics with discrete or continuous distributions. Simulation tests show that the proposed test has adequate sizes and all-around power against non-Markov chains when using a smoothed nonparametric transition density-based bootstrap approach.
Autocovariance and Autocorrelation functions
The autocovariance function compares a statistic to a time-shifted version of itself. For continuous statistics, it takes an uninterrupted form, while for discrete statistics, it takes a discrete form. It indicates the degree to which the statistic’s amplitude at one moment relates to or may be inferred from its amplitude at another time.
The covariance of the current value (xt) with the preceding value (xt-1) and the current value (xt) with the previous value (xt-1) is known as autocovariance (xt-2). It’s also referred to as. If this is a desk-bound time series, Mean will no longer alternate. as a result, the procedure will become:
Autocorrelation Function
We can address variables related to time in time collecting, such as a company’s income over time (predicting typical temperature, ozone degree, and so on). When projecting a company’s characteristic income, the beyond income will have a higher impact on the characteristic income than the previous one.
Then we utilize autocorrelation to find a correlation between the current(xt) and previous income(xt-1) and then with (xt) and (xt-2), (xt-3), and so on to find correlation within the same column. Autocorrelation is defined as the relationship between oneself and the opposite values of identical variables (features) (in our case, the relationship between (Xt and Xt-1) (Xt and Xt-2). etc…) and its miles denoted as ρ.
White Noise
For time series analysis and forecasting, the concept of white noise is critical. White noise, in the simplest terms, tells you whether or not you should optimize the model further. Because it is a sequence of random numbers, white noise is an unpredictable series. When you design a model and the residuals (the difference between anticipated and real) seem like white noise, you know you did everything you could to make the model as good as possible. On the other hand, if there are clear patterns in the residuals, there is a better model for your dataset.
For a time series to be categorized as white noise, the following conditions must be met:
· The average value is zero.
· The standard deviation does not fluctuate over time.
· There is no significant association between the time series and its lagged variant.
ARIMA Model
AutoRegressive Integrated Moving Average (ARIMA) is an acronym for AutoRegressive Integrated Moving Average. It’s a more complex version of the AutoRegressive Moving Average, with the addition of integration.
This abbreviation is descriptive, capturing the model’s major features. They are, in a nutshell:
AR stands for autoregression. The dependent relationship between an observation and a set of lagged observations is used in this model.
I stands for “integrated.” To make the time series steady, differencing raw observations (e.g. subtracting an observation from the preceding time step) is used.
MA stands for Moving Average. A model that takes into account the relationship between an observation and a residual error from a moving target.
Each of these elements is explicitly described as a parameter in the model. ARIMA(p,d,q) is a standard notation in which the parameters are replaced with integer values to immediately indicate the ARIMA model being utilized. The following are the parameters of the ARIMA model:
p: The lag order, or the number of lag observations incorporated in the model.
d: The degree of differencing is the number of times the raw observations are differenced.
q: The order of moving average, also known as the size of the moving average window.
A linear regression model is constructed with the specified number and type of terms, and the data is prepared by a degree of differencing in order to make it stationary, i.e. to remove trend and seasonal structures that negatively affect the regression model.
The Function of GARCH Models
The generalized autoregressive conditional heteroskedasticity (GARCH) method was developed in 1982 with the help of Robert F. Engle, an economist who won the Nobel Memorial Prize in Economics in 2003. GARCH is a method for estimating economic market volatility. There are several different types of GARCH modeling.
When predicting the charges and quotes of economic instruments, financial experts frequently choose the GARCH method since it provides a more real-world backdrop than other models.
As a result, the conclusions and predictive value derived from the version will no longer be valid. GARCH is a statistical model that can be used to study many types of financial data, such as macroeconomic data. This version is commonly used by financial institutions to assess the volatility of returns for stocks, bonds, and market indices.
Summary
We looked at what time series analysis is and what the essential additives of time series analysis or collection forecasting are, i.e. the constituent additives that a time collection can be divided into while performing an analysis. We also explored various time series models and how these models are essential for us.
