Homework 3
Question 7.1
Describe a situation or problem from your job, everyday life, current events, etc., for which
exponential smoothing would be appropriate. What data would you need? Would you expect the
value of alpha (the first smoothing parameter) to be closer to 0 or 1, and why?
In my work building automation for home-service businesses, a natural use for exponential
smoothing is forecasting a client's daily inbound lead volume (phone calls and web form
submissions). That forecast drives staffing for the voice agent and the dispatch schedule, so a
stable, denoised estimate of "how many leads should we expect tomorrow" is more useful than
the raw, jumpy daily count.
The data I would need is a history of daily lead counts, ideally a year or more so the model can
also pick up weekly and seasonal structure (weekends run lighter, HVAC demand spikes in
summer and winter). Each observation is just the count of leads on a given day.
I would expect alpha closer to 0 for a typical established home-service business. The true
demand level moves slowly (it changes with the local market, the season, and ad spend), while
the day-to-day count is noisy. A small alpha puts most of the weight on the smoothed history and
filters that noise, which is what I want. I would only push alpha toward 1 if the business were
changing fast (a viral campaign, a rapid expansion, a new service line), where recent observations
genuinely carry more information than older ones.
Question 7.2
Using the 20 years of daily high temperature data for Atlanta (July through October) from
Question 6.2 (file temps.txt), build and use an exponential smoothing model to help make a
judgment of whether the unofficial end of summer has gotten later over the 20 years.
Methodology
1. I read the 123 daily highs (July 1 through October 31) for each of the 20 years, 1996 through
2015, from temps.txt and confirmed the shape with head().
2. Headline model. I flattened the 20 years into one continuous series and fit a single Holt-
Winters exponential smoothing model with HoltWinters(..., seasonal =
"multiplicative"), treating the 123-day summer as the season. This estimates a level,
a trend, and a within-summer seasonal shape, and reports the fitted smoothing constants
alpha, beta, and gamma.
3. End-of-summer judgment. A single Holt-Winters model uses one shared seasonal pattern,
identical in every year, so by construction it cannot reveal a year-to-year shift in when
summer ends. To keep each year's own signal, I combined exponential smoothing with the
CUSUM change detector from Week 2:
, smooth each year's daily curve with single exponential smoothing (HoltWinters with
beta = FALSE, gamma = FALSE) to remove daily noise while preserving that year's
shape;
run a CUSUM downward-shift detector on the smoothed curve, with baseline mu set to the
mean of the smoothed July temperatures, to flag the day the temperature drops off (the
unofficial end of summer);
regress the detected end-of-summer day on the calendar year to test for a trend (a later end of
summer shows up as a positive slope).
4. Following the Week 2 CUSUM solution, I used C = 0.5 standard deviations and T = 5
standard deviations of each year's July data as the baseline tuning, then ran a sensitivity grid
over C and T to check whether the conclusion holds up.
Results
The fitted Holt-Winters smoothing constants on the full 20-year series were:
Parameter Value Reading
alpha (level) 0.615 Moderate weight on recent
observations when updating
the level.
beta (trend) 0 The optimizer found no
benefit to letting the trend
adapt; the baseline is treated
as stable.
gamma (seasonal) 0.550 The within-summer seasonal
shape updates moderately
from year to year.
SSE 68,905 Fit error over all 2,460 daily
observations.
Question 7.1
Describe a situation or problem from your job, everyday life, current events, etc., for which
exponential smoothing would be appropriate. What data would you need? Would you expect the
value of alpha (the first smoothing parameter) to be closer to 0 or 1, and why?
In my work building automation for home-service businesses, a natural use for exponential
smoothing is forecasting a client's daily inbound lead volume (phone calls and web form
submissions). That forecast drives staffing for the voice agent and the dispatch schedule, so a
stable, denoised estimate of "how many leads should we expect tomorrow" is more useful than
the raw, jumpy daily count.
The data I would need is a history of daily lead counts, ideally a year or more so the model can
also pick up weekly and seasonal structure (weekends run lighter, HVAC demand spikes in
summer and winter). Each observation is just the count of leads on a given day.
I would expect alpha closer to 0 for a typical established home-service business. The true
demand level moves slowly (it changes with the local market, the season, and ad spend), while
the day-to-day count is noisy. A small alpha puts most of the weight on the smoothed history and
filters that noise, which is what I want. I would only push alpha toward 1 if the business were
changing fast (a viral campaign, a rapid expansion, a new service line), where recent observations
genuinely carry more information than older ones.
Question 7.2
Using the 20 years of daily high temperature data for Atlanta (July through October) from
Question 6.2 (file temps.txt), build and use an exponential smoothing model to help make a
judgment of whether the unofficial end of summer has gotten later over the 20 years.
Methodology
1. I read the 123 daily highs (July 1 through October 31) for each of the 20 years, 1996 through
2015, from temps.txt and confirmed the shape with head().
2. Headline model. I flattened the 20 years into one continuous series and fit a single Holt-
Winters exponential smoothing model with HoltWinters(..., seasonal =
"multiplicative"), treating the 123-day summer as the season. This estimates a level,
a trend, and a within-summer seasonal shape, and reports the fitted smoothing constants
alpha, beta, and gamma.
3. End-of-summer judgment. A single Holt-Winters model uses one shared seasonal pattern,
identical in every year, so by construction it cannot reveal a year-to-year shift in when
summer ends. To keep each year's own signal, I combined exponential smoothing with the
CUSUM change detector from Week 2:
, smooth each year's daily curve with single exponential smoothing (HoltWinters with
beta = FALSE, gamma = FALSE) to remove daily noise while preserving that year's
shape;
run a CUSUM downward-shift detector on the smoothed curve, with baseline mu set to the
mean of the smoothed July temperatures, to flag the day the temperature drops off (the
unofficial end of summer);
regress the detected end-of-summer day on the calendar year to test for a trend (a later end of
summer shows up as a positive slope).
4. Following the Week 2 CUSUM solution, I used C = 0.5 standard deviations and T = 5
standard deviations of each year's July data as the baseline tuning, then ran a sensitivity grid
over C and T to check whether the conclusion holds up.
Results
The fitted Holt-Winters smoothing constants on the full 20-year series were:
Parameter Value Reading
alpha (level) 0.615 Moderate weight on recent
observations when updating
the level.
beta (trend) 0 The optimizer found no
benefit to letting the trend
adapt; the baseline is treated
as stable.
gamma (seasonal) 0.550 The within-summer seasonal
shape updates moderately
from year to year.
SSE 68,905 Fit error over all 2,460 daily
observations.
