Foundations for Forecasting

Basic Concepts

Basic Part of a Forecast

• Level• Growth• Uncertainty

Additive Model

t t t ty b

Multiplicative Model

t t t ty b

Forecasting Example: Gross Domestic Product

• Value of final goods and services produced in an economy during a specified period of time• Measures the size of the economy and

facilitates comparisons• Components

• Consumption• Investment• Government purchases• Net exports (exports – imports)

Nominal GDP C I G NX

Real Gross Domestic Product (GDPC1)

• Possibilities at Federal Reserve Economic Data web site (FRED)• Nominal versus real• Seasonally adjusted versus not seasonally adjusted• Frequency of data

• Data Manipulation• Linear level or no manipulation• Change• Rate of Change

Forecasts for GDP

• Last observation• Third quarter of 2014• $16,205.6 billion

• Estimate of billion dollar increase/decrease• $100 billion• Forecast: $16,205.6 + $100 = $16,305.6

• Estimate of percentage change• 0.6%• Forecast: $16,205.6 x (1 + 0.006) = $16,302.83

Vertical Axis

• Linear level in original units• Change from previous period• Change from a year ago• Percentage change• Percentage change from a year ago• Compounded annual percentage change• Continuously compounded percentage change• Continuously compounded annual percentage change• Index

Change

1t ty y

Current observation minus previous observation

Change from Previous Year

_ _ _t t n obs per yeary y

Current observation minus observation from a year ago

Percentage Change

1

1 1

100 1 100t t t

t t

y y yor

y y

Change from previous period divided by previous observation

Percentage Change from Year Ago

_ _ _

_ _ _ _ _ _

100 1 100t t n obs per year t

t n obs per year t n obs per year

y y yor

y y

Change from year ago divided by observation from a year ago

Compounded Annual Change

_ _ _

1

1 100n obs per year

t

t

y

y

Ratio of consecutive observations raised to the powerof the number of observations per year.

Continuously Compounded Rate of Change

1

log 100t

t

y

y

Natural logarithm of the ratio of consecutive observations

Continuously Compounded Annual Rate of Change

1

log _ _ _ 100t

t

yn obs per year

y

Natural logarithm of the ratio of consecutive observationsmultiplied by the number of observations per year

Alternative Forms

ˆ ht tt h ty b

 ˆ t tt h ty b h

Multiplicative:

Additive: