CAIIB ABM Module A Unit 5 : Time Series

15/01/2024

Table of Contents

CAIIB ABM Module A Unit 5: Time Series (New Syllabus)

IIBF has released the New Syllabus Exam Pattern for CAIIB Exam 2023. Following the format of the current exam, CAIIB 2024 will have now four papers. The CAIIB Paper 1 (Advanced Bank Management) includes an important topic called “Time Series”. Every candidate who are appearing for the CAIIB Certification Examination 2024 must understand each unit included in the syllabus.

In this article, we are going to cover all the necessary details of CAIIB Paper 1 (ABM) Module A (Statistics ) Unit 5 : Time Series, Aspirants must go through this article to better understand the topic, Time Series and practice using our Online Mock Test Series to strengthen their knowledge of Time Series. Unit 5: Time Series

Time Series

Secular trend is caused by basic inherent factors. Business cycle trends are mostly upward. The quality of forecast depends on the information provided by past data and its validity. Data or statistical information accumulated at regular intervals is called TIME SERIES.

There are 4 types of variations in time series

Secular Trend
Cyclical Fluctuation
Seasonal Variation
Irregular Variation.

Secular Trend

In this first type of variation the change comes over a long period of time. A steady increase in cost of living recorded by Consumer Price Index is a good example. From year to year there is a fluctuation but there is a steady increase in the trend. Let us see the series given here.

Let us try to detect patterns in the information over regular intervals of time. Then let us try to predict to cope with uncertainty.

Year	1997	1998	1999	20W	2001	2002	2003
Number	98	105	116	119	135	156	177

Observations

There is an increase over time of 7 years. But the increases are not equal.

Cyclical Fluctuation

Most common example of a cyclical fluctuation is a business cycle. Over time, there are years when business cycle hits peak above the trend line. There are also times when business activity slumps, and hits a point below the trend line.
Fluctuations in business activity occur many times, and they have irregular periods and vary widely in amplitude from cycle to cycle. The time between hitting peaks and lows are periods – it can be one or many. The cyclical moves do not follow any regular pattern, they are irregular.

Seasonal Variation

There is a pattern of change within a year. A doctor can expect the number of flu cases to increase in winter. Hill resorts can expect more tourists during summer.
These are regular patterns and can be used for forecasting the amount of flu vaccines required during winter, the doctor’s income during winter, the hotel bookings in resorts and availability of air and train bookings.

Irregular Variation

The value of the variable is unpredictable, changing in a random manner. The effects of earthquakes, floods, wars, etc., cannot be predicted.
As a result of flood, the agriculture output suffers. Then the prices go up at an unprecedented rate. This could not be predicted by using time series.
Even though we described time series as exhibiting one or another variation, in most instances real time series will contain several of these components. Then the question is how to measure them.

Trend Analysis

There are three main reasons, why we should study the trends:

We will be able to describe historical patterns, which will help us to evaluate the success of previous policies – long-term direction of the time series is given by secular trend.
Past trends will help us to project the future – some growth rate of population, GDP.
We will be able to separate the trend component and eliminate it from the series, to get an accurate idea of other components like seasonal fluctuations.

Ye = a + bx

The General equation for annual production

Ye = 139.25 + 7.536x

Estimate the no of unit ,it may produce during 2019

‘x’ is coded time

= 2(2019-2012.5) = 13

= 139.25 + 7.536 813

= 237.22

= 237 Ships loaded

Parabolic Equation:

Many series may series can be best described by curves. In these cases, the linear model doesnot adequately describe the change in the change in variable as time changes. To overcome this, we use parabolic curves.

Cyclical variation

Cyclical variation is a component of the time series, which tends to oscillate above and below the secular trend line for periods longer than a year. Seasonal variation makes a complete regular cycle within each year and does not affect one year any more than another. Once we identify the secular trend, we can isolate the remaining cyclical and irregular components of the trend. Let us assume cyclical component explains most of the variations left unexplained by the trend analysis.

Residual Method

Percentage of Trend = y actual / y trend *100
Relative cycle residual

Multiply X by 2 if n is even

Ye = a +bx

b = ΣXY/ ΣX^2

= 168/ 168 = 1

a = y¯ – b x¯

= 664/8 = 83

Ye= 83 + x

Seasonal Variation

Time series also includes seasonal variation. Seasonal variation is repetitive and predictable. This can be defined as movements around the trend line in one year or less. In order to measure seasonal variations, time intervals must be measured in small units, like days, weeks, etc.

Step 5

For modified mean : discard lowest and highest value

Total of Indices = 404.10

STEP 6:

Four quarter indices = 400

= 400/404.1 = 0.9899

Spring = 91.25 * 0.9899 = 90.3

Summer = 107.7 * .9899 = 106.6

Fall = 112.1

Winter = 91

Irregular Variation

The final component is irregular variation. After we have eliminated trend, cyclical and seasonal variations from the time series, we may still have unpredictable factor left. Irregular variations occur over very short intervals and follow random patterns. We may not be able to isolate them mathematically, but we may isolate the causes for the same. For example, an unusually very cold winter in a region may increase electricity consumption significantly. Wars may increase air and train travel because of the movement of troops. We may not be able to identify all causes. But over time, these random variations tend to correct themselves.