The post is about MCQs Time Series Analysis. There are 20 multiple-choice questions related to time series data, components of time series, least square method, objective of times series, differencing time series, decomposing a time series, and log transformation. Let us start with the MCQs time series analysis.
Online MCQs about Time Series Data Analysis and Forecasting
MCQs Time Series Analysis
A time series data is a set of data recorded at
The time series analysis helps:
A time series consists of ————.
The forecasts on the basis of a time series are ————-.
The component of a time series attached to long-term variations is termed as ————.
The sales of a shopkeeper are associated with the component of a time series
The secular trend is indicative of long-term variation towards
The linear trend of a time series indicates towards ———–.
The method of least squares to fit in the trend is applicable only if the trend is ————.
The sequence which follows an irregular or random pattern of variation is called ————.
Three are ———– main components of a time series.
The systematic components of a time series which follow regular pattern of variations are called
Which of the following is an example of irregular variation?
If a straight line is fitted to the time series, then
What is autocorrelation in time-series analysis?
In time-series analysis, what does “T” typically represent?
What is the primary objective of differencing in time-series transformation?
What is the purpose of log transformation in time-series analysis?
What is the key objective of decomposing a time series in time-series analysis?
What technique is commonly used for handling seasonality in time-series feature engineering?
Time series analysis deals with the data observed with some time-related units such as a month, days, years, quarters, minutes, etc. Time series data means that data is in a series of particular periods or intervals. Therefore, a set of observations on the values that a variable takes at different times.
Real-World Applications of Time Series Analysis
Finance: Predicting stock prices, and analyzing market trends.
Sales and Marketing: Forecasting demand, and planning promotions.
Supply Chain Management: Optimizing inventory levels, and predicting product needs.
Healthcare: Monitoring patient health trends, and predicting disease outbreaks.
Environmental Science: Forecasting weather patterns, and analyzing climate change.
We have to find a way of isolating and measuring the seasonal variations. There are two reasons for isolating and measuring the effect of seasonal variations.
To study the changes brought by seasons in the values of the given variable in a time series
To remove it from the time series to determine the value of the variable
Summing the values of a particular season for several years, the irregular variations will cancel each other, due to independent random disturbances. If we also eliminate the effect of trend and cyclical variations, the seasonal variations will be left out which are expressed as a percentage of their average.
Seasonal Variations
A study of seasonal variation leads to more realistic planning of production and purchases etc.
Seasonal Index Method
When the effect of the trend has been eliminated, we can calculate a measure of seasonal variation known as the seasonal index. A seasonal index is simply an average of the monthly or quarterly value of different years expressed as a percentage of averages of all the monthly or quarterly values of the year.
The following methods are used to estimate seasonal variations.
Average percentage method (simple average method)
Link relative method
Ratio to the trend of short-time values
Ratio to the trend of long-time averages projected to short times
Ratio to moving average
The Simple Average Method
Assume the series is expressed as
$$Y=TSCI$$
Consider the long-time averages as trend values and eliminate the trend element by expressing a short-time observed value as a percentage of the corresponding long-time average. In the multiplicative model, we obtain
\begin{align*} \frac{\text{short time observed value} }{\text{long time average}}\times &= \frac{TSCI}{T}\times 100\\ &=SCI\times 100 \end{align*}
This percentage of the long-time average represents the seasonal (S), the cyclical (C), and the irregular (I) component.
Once $SCI$ is obtained, we try to remove $CI$ as much as possible from $SCI$. This is done by arranging these percentages season-wise for all the long times (say years) and taking the modified arithmetic mean for each season by ignoring both the smallest and the largest percentages. These would be seasonal indices.
If the average of these indices is not 100, then the adjustment can be made, by expressing these seasonal indices as the percentage of their arithmetic mean. The adjustment factor would be
\begin{align*} \frac{100}{\text{Mean of Seasonal Indiex}} \rightarrow \frac{400}{\text{sums of quarterly index}} \,\, \text{ or } \frac{1200}{\text{sums of monthly indices}} \end{align*}
Example of Seasonal Variations
Question: The following data is about several automobiles sold.
Year
Quarter 1
Quarter 2
Quarter 3
Quarter 4
1981
250
278
315
288
1982
247
265
301
285
1983
261
285
353
373
1984
300
325
370
343
1985
281
317
381
374
Calculate the seasonal indices by the average percentage method.
Solution:
First, we obtain the yearly (long-term) averages
Year
1981
1982
1983
1984
1985
Year Total
1131
1098
1272
1338
1353
Yearly Average
1131/4=282.75
274.50
318.00
334.50
338.25
Next, we divide each quarterly value by the corresponding yearly average and express the results as percentages. That is,
Year
Quarter 1
Quarter 2
Quarter 3
Quarter 4
1981
$\frac{250}{282.75}\times=88.42$
$\frac{278}{282.75}\times=98.32^*$
Total (modified)
$\frac{288}{282.75}\times=101.86^*$
1982
$\frac{247}{274.50}\times=89.98^*$
$\frac{265}{274.50}\times=96.54$
$\frac{301}{274.50}\times=109.65^*$
$\frac{285}{274.50}\times=103.83$
1983
$\frac{261}{318.00}\times=82.08^*$
$\frac{285}{318.00}\times=89.62^*$
$\frac{353}{318.00}\times=111.01$
$\frac{373}{318.00}\times=117.30^*$
1984
$\frac{300}{334.50}\times=89.69$
$\frac{325}{334.50}\times=97.16$
$\frac{370}{334.50}\times=110.61$
$\frac{343}{334.50}\times=102.54$
1985
$\frac{281}{338.25}\times=83.07$
$\frac{317}{338.25}\times=93.72$
$\frac{381}{338.25}\times=112.64^*$
$\frac{374}{338.25}\times=110.57$
Total (modified)
261.18
247.42
333.03
316.94
Total
Mean (modified)
$\frac{261.18}{3}=87.06$
$\frac{247.42}{3}=95.81$
$\frac{333.03}{3}=111.01$
$\frac{316.94}{3}=105.65$
399.52
* on values represents the smallest and largest values in a quarter that are not included in the total.
Statistical Software for Seasonal Variation
Several statistical software packages can automate these calculations for you. Popular options include:
Python libraries like Pandas and Statsmodels
R statistical computing environment
Excel with add-in tools like Data Analysis ToolPak
