Individual Income Tax - Report Example

Introduction

In most countries, there has been a spectated, dramatic deterioration in public resources and state finances. The latter raises concerns concerning the capacity of the government to employ, educate, and support community-based services such as health. Since recessions affect states differently by using different tax structures, most employees are affected differently. Due to this, there arises the need for examining how changes in state revenues affect the expenditure; the instance demand-side factors are being controlled that impact and influence program utilization. The paper focuses on calculating the time series exponential smoothing for individual income tax.

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Due to declines in the state revenues, there results in long and short-term cuts in employee's salaries following the increased taxes. The time series analysis allows policy analysts and public administrators to determine the values of a particular variable across a specific interval of time (Hamilton, 2020). For example, the values involved are the yearly income tax figures of individuals. Using a time series analysis, analysts and administrators can acknowledge the patterns adopted in the values and later allow them to predict the future per the existing and historical designs.

Exponential Smoothing

Even with the time series analysis to predict future values, exponential smoothing is a requirement to accomplish making these future projections (Köppelová & Jindrová, 2019). It is a way of ensuring that the expected date is smoothed out to make forecasts in every presentation. Exponential smoothing is mostly used if the data involved does not have a clear pattern. For example, from 2014 to 2019, the data for individual income tax is not consistent (Hamilton, 2020). Even though it shows that it is continuously increasing every year, no in-depth prediction can be made further.

Damping Factor

For this exponential smoothing, the damping factor used can be confusing. The damping factors are employed to smooth out the graph and have a value ranging between 1 and 0 (Zou et al., 2018). The alpha level used was zero; hence a larger damping factor was obtained. If a smaller damping factor were used, it would mean large alpha values were used. Based on the graph, the peaks and valleys were not existent; a horizontal straight line was obtained.

Using the Data Analysis Toolpack in excel, exponential smoothing created for six observations from 2014 to 2019 gave more weight to the most recent event. In this case, the previous observations are taken into account to favor the recently made observations (Zou et al., 2018). Forecasts sincerely rely on the most recent observations for predictions.

The horizontal straight line gives long-term forecasts per the SMA model and not the random walk model disregarding growth. It is essential to note that the confidence intervals diverge reasonably (Zou et al., 2018). Additionally, they are substantially narrower for the random walk model than the confidence intervals.

An SES model can be defined as a unique Arima model case. The latter provides a fundamental baseline to calculate confidence intervals. The above chart is supported by the SES model, which relies on an Arima model that does not possess the nonseasonal difference, a constant term, and an MA(1) term (Fulcher, 2018). The latter used is obtained as the damping factor; it correlates to the amount or quantity 1-α. Thus the MA(1) term used was one since the value of α was 0.

The assumption of having a constant linear trend, which is non zero, is implemented in the chart. From the chart, it is evident that the model had an MA(1) term and one nonseasonal difference with a constant (Hansun, 2016). Based on the chart, the long term forecasts would possess a trend that equates or equals to the average trend obtained over the five years, the entire estimation period. Even though this is not supposed to be done in association with the seasonal adjustment, the latter is disabled to ensure the model type is dedicated to ARIMA (Hansun, 2016).

However, an exponential trend having a constant long term aspect can be added to an exponential smoothing model that is simple: having or not having a seasonal adjustment (Köppelová & Jindrová, 2019). The option occurs in the forecasting procedure by ensuring that the adjustment inflation component is used. The appropriate" inflation" rate per period, defined as growth percentage, is estimated as the slope's coefficient on the linear trend model connected to the data used in transforming the natural logarithm (Hansun, 2016). In this case, it relied on separate independent information regarding prospects of long term growth.

Trend Extrapolation

It is crucial to understand that data can be adjusted for inflation, if necessary. If this is necessary, then it becomes imprudent to extrapolate linear trends that are short term into the future. Due to varied causes like increased tax rates, there is a high probability that the trends will slack in the future. Due to this, the simple exponential smoothing performed gave better out of sample than expected. Despite having a naïve trend extrapolation, which is horizontally placed, it is viable for determining the futuristic trend (Guan et al., 2018). The damped trend modifications regarding the smoothing model for linear, exponential variables are mostly applied to introduce some sense of conservatism to the trend projections.

Outliers

In the time series, outliers have the capacity and potential of influencing or affecting the estimates of the parameter alongside the forecasts made, especially when exponential smoothing is applied. There are different sets of outliers that can be integrated into linear innovations models. They are crucial since they assist in identifying some critical aspects regarding exponential smoothing methods (Köppelová & Jindrová, 2019). In this case, the types of outliers viable to occur included level shift, additive outlier, and transitory change. The model is adept at modeling trends and seasonality; hence it is challenging to predict and forecast outliers.

Conclusion

In conclusion, the exponential smoothing of data in time series analysis decreases in weight to the oldest observations from the newest. The older data, in our case, data obtained in 2014, has minimal priority or weight compared to data obtained in 2019. The more recent data is observed and taken as more relevant. Due to this, it is assigned more weight. Smoothing constants or smoothing parameters are usually depicted by α, and they assist in identifying each observation's weight. Even though Exponential smoothing has been applied to make long term predictions, it is mostly employed to forecast short term data. Therefore, long term forecasts achieved using exponential smoothing can be unrealistic and unreliable.

References

Hamilton, J. D. (2020). Time series analysis. Princeton university press.

Zou, Y., Donner, R. V., Marwan, N., Donges, J. F., & Kurths, J. (2019). Complex network approaches to nonlinear time series analysis. Physics Reports, 787, 1-97.
https://www.sciencedirect.com/science/article/pii/S037015731830276X

Fulcher, B. D. (2018). Feature-based time-series analysis. In Feature engineering for machine learning and data analytics (pp. 87-116). CRC Press.

Hansun, S. E. N. G. (2016). A new approach of brown’s double exponential smoothing method in time series analysis. Balkan Journal of Electrical & Computer Engineering, 4(2), 75-78. https://www.researchgate.net/profile/Seng_Hansun/publication/309165009_A_New_Approach_of_Brown's_Double_Exponential_Smoothing_Method_in_Time_Series_Analysis/links/5809876308ae993dc050a495/A-New-Approach-of-Browns-Double-Exponential-Smoothing-Method-in-Time-Series-Analysis.pdf

Guan, P., Wu, W., & Huang, D. (2018). Trends of reported human brucellosis cases in mainland China from 2007 to 2017: an exponential smoothing time series analysis. Environmental health and preventive medicine, 23(1), 1-7. https://environhealthprevmed.biomedcentral.com/articles/10.1186/s12199-018-0712-5

Köppelová, J., & Jindrová, A. (2019). Application of exponential smoothing models and arima models in time series analysis from telco area. AGRIS on-line Papers in Economics and Informatics, 11(665-2019-4145), 73-84. https://ageconsearch.umn.edu/record/294568/.