I need two comments, each part is around 100 words comment.

Part 1:

**Question 1**

There are a few actions that would be taken in the preliminary investigation of the time series to inform the choice of the forecasting method. Time series incorporates the number of observations collected over a successive period of time. By observing a variable or sets of variables for a specific period of time and record the behavior of the variables, then a trend is established against time. One of the actions that would be undertaken is to identify the values and how they change over time. A large amount of series data is dependent on past values. Current trends provide information about the behavior of variables (Ho & Ting, 2015). Variables such as exchange rates are lagged values that could be regressed over one or many lagged values in order to predict the future and current values of the variable. Missing data can be filled with past data, which can be calculated by taking averages.The second action would be to identify time periods.Time periods can be yearly, monthly, weekly, and daily. When forecasting future data with past data, lag operators could be used in forecasting methods to quantify future, present, and past values that are linked to one another. Further, the univariate time series is a progression of the measurements of the same variables obtained over time. Often, the measurement is made at regular intervals. A major defining characteristic of a time series is that ordering matters. The importance of ordering in time series is that a change in order could also change the meaning of the data due to the dependency. As such, identifying the time periods between values or variables is essential in determining the right forecasting method to use.

**Question 2**

The classical decomposition is a simple procedure that forms the starting point for most other methods of time series decomposition. Two forms of classical decompositions can be used; multiplicative decomposition and additive decomposition. The additive decomposition method would be preferred when the seasonal variations of variables are relatively constant in the period under consideration. In additive decomposition method, the variance of data does not change over different values of the time series. The trend line is a straight line, the additive approach is a straight line, and the seasonality has the same amplitude and frequency. The individual values are differentiated and added together to model the data. A real-life example that would call for the use of additive decomposition is a business that experiences seasonal variations in sales over specific periods. For example, a business that sells umbrellas is likely to experience a boom in sales during the June-August period. An additive decomposition method would be the most appropriate for the business given that the seasonal variation is about the same magnitude across time.

The multiplicative method would be preferred when variation increases over the period under consideration. In this method, seasonal components and the trend are multiplied and then added to the error component. Unlike the additive method, the multiplicative method results to a curved line. A real-life situation that would call for the application of multiplicative decomposition is the forecast of the quarterly earnings of a business. The quarterly earnings data varies significantly based on a range of factors including the strategies of the business, the life-cycle stage, external factors such as regulatory forces and competition. Multiplicative decomposition would be the most appropriate because the seasonality has a decreasing or increasing amplitude and frequency over time.

Part 2:

__Question 1:__** Suppose that you are given a time series and are asked to forecast the values of the time series during one or more of the future periods. Explain a few of the actions that you will undertake as your preliminary investigation of the given time series before you decide which particular forecasting method you should use****.**

Hello everyone,

Being able to forecast data based on trends and patterns is one of the most powerful tools available in data analytics today. Although there are a variety of methods prior to working with dataset, if I was provided with the opportunity to forecast the values of a given time series during one of more future periods, I would perform the following actions:

- First, I would review the dataset at a high-level to understand the different components, and the message that the data is intending to deliver. I would particularly look for trends in the data, to get a better sense of this message. In addition, I would want to know the overall data structure, as well as the format of the data within the columns.
- Next, I would start to manipulate and tidy up the data. I would use a variety of packages such as “dplyr” and “tidyr” to ensure that my data is well-organized and clean for analysis. This would include ensuring that there are no rows or columns with missing values.
- Finally, I would validate whether the data is ready for a time series analysis. I would ensure there is enough historical data to work with, in the first place. In addition, I would want to know which specific questions the dataset, once analyzed through a time series, can help with answering.

Once I have completed performing the above actions, I would have a better understanding of the data. I would then choose the appropriate method for forecasting, which would include either of Moving Average, Regression Analysis, or Exponential Smoothing.

__Question 2__**: In many applications, a time series decomposition (i.e., time series filtering) is used to separate or decompose a time series XtXt into its trend, seasonal, and irregular components. In some of these applications, the decomposition relationship is assumed to be additive; while in other applications the decomposition relationship is assumed to be multiplicative. Explain in what situations you would prefer to use an additive decomposition method, and in what situations you would prefer to use a multiplicative method in your time series decomposition. Furthermore, mention a specific example of a real-life time series that is of interest to some enterprise, and for which you would prescribe a multiplicative decomposition.**

**Note: an additive decomposition of XtXt is a decomposition of the form: Xt=Trendt+Seasonalt+IrregulartXt=Trendt+Seasonalt+Irregulart; and a multiplicative decomposition is a decomposition of the form: Xt=Trendt×Seasonalt×IrregulartXt=Trendt×Seasonalt×Irregulart.**

In the case of a time series analysis, I would choose between various models depending on whether there is seasonality or not, and whether or not a trend is noticed. If there was no seasonality and no trend, I would choose either the Single Moving Average or the Single Exponential Smoothing models. However, if there was a trend despite no seasonality, I would pick one of the Double Moving Average or Double Exponential Smoothing models. On the other hand, if seasonality was present, but no trend, the Seasonal Additive and Seasonal Multiplicative models would be chosen. If seasonality was present with a trend, I would choose either one of the Holt-Winters Additive or Holt-Winters Multiplicative models.

Diving deeper in to the Seasonal and Multiplicative models, if I was presented with a time series dataset, for which the dependent variable that changed very slightly over a period of time, and stayed constant for the most part, I would choose the Seasonal Additive Model. On the other hand, if there was a noticeable trend being present over the entire time series, then it would make sense to use the Seasonal Multiplicative Model.

One of the most common real-life examples for time-series analysis is the stock market. If there are specific stocks, which increase over time, those stocks become more favourable, and in turn, start to get followed. To understand this relationship more closely, a time series analysis would be used. Given that the change in stock price is seen as a trend over time, the Multiplicative model would be ideal.

As a result of the different criteria being presented, I would choose the appropriate models for my time series analysis. By doing so, I would be able to better analyze the relationship of a given independent variable as it changes over time.