University Statistics: Time Series Analysis DB 1-4 Assignment

This statistics assignment solution explores key concepts in time series analysis. It begins by defining time series data, contrasting it with other statistical methods like linear regression, and outlining the forecasting process. The assignment then delves into the significance of data preparation, detailing its purpose, importance, and the indicators that signal a dataset requires additional preparation. Next, it compares and contrasts exponential smoothing methods, differentiating between non-seasonal and seasonal data series, and providing examples of model suitability. Finally, the solution discusses Autoregressive Integrated Moving Average (ARIMA) models, outlining their assumptions and offering examples of when one model is preferable over another. The assignment covers various aspects of time series analysis, including data preparation, smoothing techniques, and ARIMA models, providing a comprehensive understanding of the subject.

Running head: STATISTICS 1
DB 5
Student’s name
University affiliation
Author’s note

STATISTICS 2
DB 1 SUMMARY
These discuses about the patterns and characteristics of time series. Time series is data
that has been observed and recorded over a specific period. It is used when remarks are made
constantly over 50 or more periods. The remarks can be from a single case, but in most cases, it
is derived from multiple instances. The main goal of the analysis is to categorize patterns in the
order of numbers over time, which are interrelated, but offset in time.
The analysis involves three steps, identifying, estimating, and diagnosis. Identification
involves examination of the Partial Autocorrelation Functions (PACFs) and Autocorrelation
Functions (ACFs) (Dalinina, 2017). Long-time series have tendencies for measures, which vary
periodically and are referred to seasonality.
Time series analysis is the most applicable autocorrecting analysis for data as compared
to multiple regressions. First, there is an unequivocal violation of the assumption of
independence error. Secondly is that the patterns are either incomprehensible or spuriously
develop the effect of an intervention lest accounted for in the model.
DB 2 SUMMARY
This discusses and analyses the significance and prominence of data preparation with
regards to time series analysis. It is essential to prepare data before analyzing and getting it to a
comfortable set, which can be read and interpreted (Dalinina, 2017). Data preparation involves
gathering raw data from various sources, combining and reefing it so that it can be adjusted and
organized for easy analysis. This can be done by IT specialists or in business departments.
Data preparation is necessary due to multiple reasons. Information obtained might be in
different formats hence essential to group them appropriately. Also, the data would not found in
one location, thus the need for preparation. Lastly, it avoids discrepancies, errors, and lack of

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interest in the final goal. Importantly, data is prepared to ensure quality is obtained. To ensure
quality data, there must be presence of accuracy, complete data set, consistency, timeliness, and
representatives.
DB 3 SUMMARY
This section differentiates and compares between the non-seasonal and seasonal data
series. It starts by defining smoothing of time series as a process of dividing noise and signal
from a data set to gain an estimate for the signal. The mostly used leveling model is exponential
smoothing. Here, weights are assigned to the newest and oldest observations. As such, old data
has fewer weights, while new data carries more weights (Chaterjee, 2018). Exponential
smoothing is designed to reduce the weight and have less focus on old data as it increases the
emphasis on recent weight data.
There are different types of smoothing exponentials. When there is no tendency or
seasonal pattern in forecasting, a single exponential method is used. While the mean of the data
may slowly change, the data display may remain the same. The contrary to the single exponential
method is double exponential smoothing. It displays a trend; hence, the most reliable trend used.
However, it is more complicated than the single exponential method since it adds the forecast
equation and two smoothing equations to the procedure (Chaterjee, 2018). Other types of
smoothing methods include Holt winters seasonal method. It comprises of two methods that
encompass multiplicative and addictive methods. For time series with regular seasonal
variations, the addictive holt-winter method is used. The multiplicative holt-winter method
applies to time series with collective seasonal changes.
DB4 SUMMARY

STATISTICS 4
It talks about Autoregressive Integrated Moving Average Models. They are prevalent
forecasting approaches used with time series. To reduce the time series stationary, they are used
when time series is non-stationary. ARIMA models are classified into two models. These include
non-seasonal ARIMA (SARIMA) and seasonal ARIMA, commonly known as p.d.q. The three
parameters in seasonal ARIMA stands for the number of lags, number of differencings, in the
integration and the lag error component respectively. Also, SARIMA comprises of the three
parameters only that it has complex models, which rely on historical values.
Shorthand multiplicative SARIMA equation is represented by ARIMA (p.d.q.) * (P.D.Q.)
S. S stands for the number of periods in a season.
Seasonal ARIMA models should be used for univariate data within a seasonal pattern.
For instance, it can be used during forecasting, predicting the number of passengers a ferry will
route at a specific time of the year. On the other hand, non-seasonal ARIMA should be used for
univariate data with a trend. An example includes forecasting the number of mobile handset
users in a specific region such as the southern hemisphere.

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References
Chaterjee, S. (2018, February 5). Time series analysis using ARIMA model in R. Retrieved May
18, 2019, from Data Science Plus: https://datascienceplus.com/time-series-
analysis-using-arima-model-in-r/
Dalinina, R. (2017, January 10). Introduction to forecasting with ARIMA in R. Retrieved June 6,
2019, from Data Science: https://www.datascience.com/blog/introduction-to-
forecasting-with-arima-in-r-learn-data-science-tutorials