Moving deep down into the time series analysis, I have gone through the different topics such as autocorrelation, forecasting, and cyclical analysis. Also, while thinking about the regression analysis, I came to a decision that conventional linear regression may not be the best option for time series research, particularly if the data shows seasonality, trends, or temporal dependencies. The essential premises of linear regression—independence and homoscedasticity—are frequently broken by time series data. Using autoregressive integrated moving average (ARIMA) models or other time series forecasting techniques might be a better strategy for time series regression.

Autocorrelation Function (ACF): The Autocorrelation Function (ACF) is a statistical tool that is used to determine the correlation between a time series and its own lagged values. It makes it easier to find patterns, trends, and seasonality in the data. The ACF plot displays correlation coefficients for different lags, allowing one to pinpoint significant delays and potential autocorrelation patterns in the time series.

Forecasting: To start the forecasting process, it is often necessary to use the most recent observed value from the historical data.Iterative Prediction: For every subsequent time interval, the forecast for the subsequent observation is simply the most recent observed value. The model assumes that any changes or deviations are random and unpredictable.Evaluation: Metrics like Mean Absolute Error (MAE), Mean Squared Error (MSE), or Root Mean Squared Error (RMSE) are frequently used to assess the performance of the random walk model by comparing the projected values to the actual observations.

Cyclical: In time series analysis, cyclical analysis is the study of long-term periodic patterns or variations that are not always associated with the regular seasons based on the calendar. Cyclical patterns, in contrast to seasonal patterns, are linked to business or economic cycles and have longer durations. Seasonal patterns repeat at specified intervals, such as daily, monthly, or yearly. It mainly emphasizes on the areas like financial markets, investment and business decision making, and economy models.