Answer To: You have to submit 2 files :Answer Report: In this, you need to submit all the answers to all the...
Mohd answered on Apr 19 2023
We have two time series data to build and test the different time series forecasting model in order to achieve highly accurate result for future prediction. We have used Exponential smoothing, Holt winters method, simple linear regression and ARIMA/SARIMA models. For stationarity test we have used Augmented Dicky Fuller Test. We have also used n order differencing techniques to transformed the time series data from non-stationary to stationary data. We have used root mean squared error as performance evaluation metrics.
On the test dataset, simple linear regression with the prediction of soft drink production had the lowest RMSE. In order to obtain the stationary time series data, we additionally performed some differentiating. First order differencing has allowed us to obtain the needed stationary data in both situations.
We used an augmented dickey fuller test to verify the stationarity of our data. Simple Exponential Smoothing with default parameters produced the lowest RMSE in our second dataset of shoe sales, whereas Holt Winter’s Model produced the greatest RMSE.
A forecasting technique for univariate time series data is exponential smoothing. With this strategy, predictions are weighted averages of historical observations, with the weights of earlier observations decreasing exponentially. The study may now include model data with trends and seasonal components thanks to various forms of exponential smoothing. It has had great popularity among analysts as a rapid technique to provide precise projections in a variety of disciplines, especially in business. Additionally, it is utilized in signal processing to filter high-frequency noise and smooth signals.
Only the level component is estimated using simple exponential smoothing. Consider the level component to be the average or normal value. For each observation, this procedure changes the level component. It only utilizes one weighting parameter, alpha (), because it only models one component. The amount of smoothing is controlled by this variable by altering how soon the level component catches up with the most recent data.
The range of possible alpha values is 0 to 1, inclusive. Because they average out changes over time, lower values lend greater weight to historical observations and generate smoother fitted lines. Higher values limit the degree of averaging by the earlier data, which results in a more jagged line since they place a higher emphasis on the current data.
To eliminate the irregular fluctuations (noise) and capture the underlying pattern, you usually wish to smooth the data. However, you don't want to smooth things out too much and lose important details! Nevertheless, while selecting alpha, apply your subject-matter expertise and professional standards. = 0.2 is a typical default value.
Holt Winters’s Method:
For univariate time series data, triple exponential smoothing can describe the seasonality, trend, and level components. Data patterns known as seasonal cycles appear over an average number of observations. Another name for triple exponential smoothing is Holt-Winters’s exponential smoothing. This approach incorporates the gamma () parameter to take the seasonal component into consideration. You must provide the length of the seasonal cycle for this approach. These durations could be, for instance, weekly (7), monthly (12), or quarterly (4). Seasonality in the triple exponential smoothing can be multiplicative or additive. The pattern of multiplicative seasonality is that the magnitude grows as the data grow. Even when the data vary, additive seasonality depicts a seasonal pattern with a consistent scale.
The most popular statistical tests used to determine whether a particular Time series is stationary or not are the Kwiatkowski-Phillips-Schmidt-Shin test (KPSS test) and the Augmented Dickey-Fuller test (ADF Test). When examining the stationarity of a series, these two tests are the most often applied statistical tests. Stationarity is a crucial component of time series. A model cannot predict on non-stationary time series data, hence the first step in ARIMA time series forecasting is to calculate the number of differences needed to make the series stationary. Let's attempt to comprehend a little more thoroughly.
The term "stationary series" refers to a series whose statistical characteristics, such as mean, variance, covariance, and standard deviation, do not change over time or are not affected by the passage of time. To put it another way, stationarity in time series refers to a series without any elements of trend or season. It enables us to use forecasting models like the SARIMA (Seasonal ARIMA) model or the ARIMA (Auto Regressive Integrated Moving Average) model that better reflect our understanding of the data.
Augmented Dickey-Fuller testing
Strong assumptions about your data are made throughout statistical testing. They can only be used to provide information about how easily or not easily a null hypothesis may be rejected. For a given problem to have any significance, the outcome must be understood. They do, however, offer a rapid examination and confirmatory proof of the time series' stationary or non-stationary nature. A unit root, which can be problematic in statistical inference using time series models, is a characteristic of some stochastic processes (such as random walks) in probability theory and statistics. The unit root is...