Data Analysis: Chapter 14: Time-Series Analysis

A common choice of a smoothing constant is ___.

.2

The smoothing constant, a, can be any value between _______ and ______.

0 and 1

In a small neighborhood community, it has been documented that homes sales vary quarterly throughout the year and that the sales have been consistently increasing over the past 5 years. The quarterly indexes were found to be 0.73 for quarter 1, 0.90 for quarter 2, and 1.4 for quarter 3. What is the value of the fourth quarter seasonal index? Round to two decimals.

0.97

To compute a trailing moving average forecast with m=4 for the 5th time period, you would need to use data from period ______.

1-4

When using Excel's Data Analysis Tool to compute the exponential smoothing forecast, the damping factor is equal to ________.

1-a

Exponential smoothing works well when ________.

1. data is trendless 2. many SKUs are forecast each time period

A linear trend is typically used for _______.

1. simple modeling 2. short-run modeling 3. baseline forecasting

A regression model with monthly seasonal binary variables would have ___________ binaries.

12

To compute a centered moving average with m=3 for the 5th time period, you would need to use data from periods ______.

4-6

Jonah's Autos wanted to analyze their number of weekly car sales. An employee in the accounting department fitted a linear trend to the data. The model is yt=20+5t. The number of cars sold is increasing by an average of _______ cars per ________.

5; week

Match the forecast error measure to its "pro"

R2: common, unit fee MAPE: unit-free (%) and intuitive MAD: same units as yt, intuitive MSD: greater weight on large errors SE: same units as yt, can be used for confidence intervals

The components of a time series can be modeled in two ways. The ________ model is used for short-run series with values that have similar magnitude. The _______ model is used for long-run series with increasing or decreasing magnitude.

additive; multiplicative

forecasting

an analytical way to describe a "what if" future that might confront the organization - helps decision makers become aware of trends or patters that require a response - can facilitate organizational communication

time-series variable

consists of data observes over n periods of time - denoted as Y

multiplicative model

data of increasing or decreasing magnitude (long-run or trended data) with constant percent growth or decline - more useful for forecasting financial data, particularly when the data vary over a range of magnitudes.

additive model

data of similar magnitude (short-run or trend-free data) with constant absolute growth or decline - attractive for simplicity

Observations in a time series data set are divided by a seasonal index in order to ______ the data set.

deseasonalize

Observations in a time series data set are divided by a seasonal index in order to _______ the data set.

deseasonalize

One of the potential issues with a trailing moving average is that ______- weight is given to the recent m observations

equal

If the adjusted seasonal index is 1.00 for season A, this implies that values for season A are _____ the average of all the seasonal values.

equal to

Principle of Occam's Razor

given two sufficient explanations, we prefer the simpler one

The value of the smoothing constant can be determined by applying a criteria such as ______ the error measure.

minimizing

The value of the smoothing constant can be determined by applying a criteria such as _______ the error measure.

minimizing

Exponential smoothing is a type of moving average used for _____ -period- ahead forecasting.

one

Forecasting is part of a company's _________ process and helps ___________ makers analyze trends and patterns so they can deal with contingencies.

planning; decision

A ______ trend model is often used when the time series has a turning point at some time period

quadratic

In a small neighborhood community, it has been documented that home sales vary quarterly each year and that the sales have been consistently increasing over the past 5 years. A regression model with quarterly binary predictors was developed: Sales = 49.02 + 0.74time-2.19Qtr1+1.39Qtr2+2.56Qtr3. If the coefficient estimates obtained in the regression are statistically different from zero, an interpretation of the coefficient of Qtr1 reveals that _______.

the home sales are approximately 2.19 lower in quarter 1 and in quarter 4 on average

n

the number of time periods

periodicity

the time interval over which data are collected - decade, year, quarter, month, week, day, hour

yt

the value of the time series in period t

An index number allows comparisons between two or more ______-series variables.

time

A variables whose observations are recorded in a consistent sequential order is considered a _________ _________ variable.

time series

Why are moving average smoothing techniques used in forecasting?

to reduce the impact of random fluctuations

True or False: An exponential trend model can be fitted by transforming the response variable y using In(y) and then using regression analysis to find the slope and intercept. The exponential model parameters are a=e^intercept and b=slope.

true

True or False: An exponential trend model is commonly used for financial data because analysis often compare percentage growth rates for revenue, costs, or salaries.

true

True or false: Excel will calculate TMA values for a time series from the Add trendline option or from the data analysis tool.

true

True or false: Relative indexes allows one to compare changes over time regardless of variable units.

true

quadratic trend model

y=a+bt+ct^2 - the t^2 term allows a nonlinear shape. It is useful for a time series that has a turning point or that is not captured by the exponential model

linear trend model

yt = a+bt - useful in time series that grows or declines by the same amount (b) in each period - fitted in the usual way by using the ordinary least squares formulas

exponential trend model

yt = ae^bt - useful for a time series that grows or declines at the same rate (b) in each period - often preferred for financial data or data that cover a longer period of time

In a small neighborhood community data collected over a 20 year period has revealed that home sales vary quarterly each year. It we construct a regression model with seasonal binary variables, the model would be: _____________.

sales - b0 + b1time + b2Qtr1 + b3Qtr2 + b4Qtr3

When a time series shows a pattern of repetitions over a one year period that can repeats monthly or quarterly we say the time series is _________.

seasonal

When a time series shows a pattern of repetitions over a one year period that can repeats monthly or quarterly we the time series is ______.

seasonal

If today's consumer price index were equal to 212 this means _______.

that on average prices are now slightly more than double those in 1982-1984

A measure of fit for an exponential trend model is _______.

the coefficient of determination

y1, y2...yn

the data set for analysis

exponential smoothing

- special kind of moving average - used for ongoing on-period-ahead forecasting for data that have up and down movements but not consistent trend

trailing moving average

- the simplest kind of moving average Y(hat)t=yt+yt−1+...+yt−m+1/m - smoothes the past fluctuations in the time series, helping us see the pattern more clearly

trend (T)

a general movement over all years - change over a few years is not a trend - some trends are steady and predictable

Irregular (I)

a random disturbance that follows no apparent pattern - also called the error component or random noise reflecting all factors other than trend, cycle, and seasonality - large error components are not unusual

seasonal (S)

a repetitive cyclical pattern within a year - for example, many retail business experience strong sales during the fourth quarter because of Christmas

cycle (C)

a repetitive up and down movement around the trend that covers several years

Choose the definition of the cycle component of a time series

a repetitive up and down movement that covers several years

Choose the definition of the trend component of a time series

a sustained movement in one direction over time

t

an index denoting the time period

To measure relative change over time in a variable _____.

an index is calculated by choosing a base period and taking a ratio of the current period to the base period

Quantitative forecasts make ________ explicit by forcing the analyst to clearly state and explain their __________.

assumptions; assumptions

centered moving average

looks both forward and backward in time, to express the current "forecast" as the mean of the current observation and observations on either side of the current data y(hat)t=yt−1+yt+yt+1/3

Choose the definition of the irregular component of a time series.

movement with no apparent pattern also called noise

Jonah's Autos has analyzed the number of used cars on their lots over the past 10 years. The model is yt=987-35.4t+3.78t^2. This model indicates that _______.

the number of cars decreased and then increased over time

planning

the organizations attempt to determine actions it will take under each foreseeable contingency

deseasonalize

when the data periodicity is monthly or quarterly, we should calculate a seasonal index

in the exponential smoothing method, the simple approach for initializing the process is to let F1 = _______

y1

In a small neighborhood community, it has been documented that home sales vary quarterly throughout the year and that the sales have been consistently increasing over the past 5 years. The quarterly indexes were found to be 0.73 for quarter 1, 0.90 for quarter 2, and 1.4 for quarter 3. Also, a trend analysis revealed the following model yt=10+3.04t would reflect how the number of sales have been gradually increasing each year. What would be the forecast for the number of home sales for the second quarter of yeah 6?

0.90[10+3.04(22)]= 69.2

To calculate a seasonal index there are 4 steps involved. Name the 4 steps in order.

1. Calculate the centered moving average for each period 2. compute seasonal ratios by dividing observed values by the CMA 3. Average the ratios by time period over the multiple years to get a raw index 4. Adjust the raw indexes so they sum to 4 (for quarterly data) or 12 (for monthly data)

5 measures of fit (Table 14.9 in section 3)

1. Coefficient of determination 2. Mean of absolute percent error (MAPE) 3. Mean absolute deviation (MAD) 4. Mean squared deviation (MSD) 5. Standard error (SE)

For time series data that exhibit a trend or have seasonal components one can use ________.

1. Holt's method for adding a trend component 2. Winter's method for adding both a trend and a seasonal component

Nancy is the manager of a gas station in Cleveland, Ohio. She is collecting various types of data about her business. Identify the time series variables.

1. Nancy counted the number of customers each Saturday for the past 6 months 2. Nancy collected the price of a gallon of gas from every gas station in Cleveland on the first day of the month for the past year

Time series models can be classified as ______

1. smoothing models 2. decomposition models 3. trend models

types of moving average

1. trailing 2. centered

Jonah's Autos wanted to analyze their number of weekly car sales. An employee in the accounting department fitted a linear trend to the data. The model is yt = 20+5t. The forecast for week 6 is _______ cars sold.

20+5(6)=50

In a small neighborhood community, it has been documented that home sales have 3 distinct seasons per year. After deseasonalizing the data a seasonal index of 1.34 was calculated for the second season. This seasonal index implies that homes sales are __________% ________________ than the average annual sales.

34%; greater

Choose the definition of the seasonal component of a time series.

A repetitive up and down pattern within a year, week, or day

To determine if a linear trend model is a good fit to past data one would look at the value of ____.

R^2

True or False: A linear trend model can be fitted using Excel's regression function and letting time be the response variable

false

The time interval over which time series data are collected is called the ________. Common time intervals are monthly, yearly, or quarterly.

periodicity

three general patters of trends

1. growth 2. stability 3. decline

Criteria for selecting a trend model for forecasting include:

1. Occam's razor: Would a simpler model suffice? 2. Overall fit: How does the trend fit the past data? 3. Believability: Does the extrapolated trend "look right?" 4. Fit to recent data: Does the fitted trend match the last few data points?

Order the steps used to fit a trend on Excel

1. Plot a line chart of the time series data with the time variable on the horizontal axis 2. from the chart tools select the layout tab 3. click trend line 4. click trend line options 5. choose the type of trend line and check off Display Equation on chart

steps to deseasonalize data for time-series observations

1. calculate a centered moving average (CMA) for each month (quarter) 2. Divide each observed yt value by the CMA to obtain seasonal ratios 3. Average the seasonal ratios by month (quarter) to get raw seasonal indexes. 4. Adjust the raw seasonal indexes so they sum to 12 (monthly) or 4 (quarterly) 5. Divide each yt by its seasonal index to get deasonalized data

to ensure good forecast models

1. maintain up to date databases of relevant data 2. allow sufficient lead time to analyze the data 3. state several alternative forecasts or scenarios 4. track forecast errors over time 5. state your assumptions and qualifications and consider your time horizon 6. don't underestimate the power of a good graph

subtler trends within each general pattern

1. steady linear rate 2. increasing rate 3. decreasing rate 4. growth and level off 5. growth towards an asymptote

time-series decomposition seeks to separate a time-series Y into four components:

1. trend (T) 2. cycle (C) 3. seasonal (S) 4. irregular (I)

Jonah's Autos has analyzed their annual revenue for the past 6 years. The model is yt=2.56e^0.165t. The revenue is increasing at a rate of _____ each year.

16.5%

Jonah's Autos has analyzed their annual revenue (in millions) for the past 6 years. The model is yt=2.56e^0.165t. The revenue expected revenue in two years is __________.

2.56e^.165(2) = 3.56 million

Linear and exponential trend models are widely used because they have only ______ parameters whereas the ________ model is used for time series that show a turning point.

two; quadratic

The Dow Jones Industrial Average is a ______ index.

weighted

The CPI is an example of a Laspeyers index which applies ________ to reflect the importance of various items that make up a "basket" of goods and services.

weights