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Chapter 10 ● Advanced Methods of Forecasting
Exercises 10.7, 10.9, 10.10, and 10.11 Solutions
Authors’ note (Sept. 2012): The solutions to 10.7, 10.9 and 10.11 are at best incomplete!
10.7 Using the data set Gasprices_full.xlsx,
a. Test whether Crude, CPI, and Unemployment are stationary variables.
b. Develop a regression model for Unleaded, using the methods of Chapter 9.
c. Develop a three-variable VAR model that includes the price of Unleaded. In so doing, include only
those variables you expect to have an economic impact on the unleaded price. Use a maximum of two
lags.
d. Examine whether there is evidence for including lags longer than two in your model.
e. Evaluate the forecasting performance of your chosen model.
f. Develop a model in differences (for any of the nonstationary variables). Is this model a "better" model
than the model developed in levels in parts (b) and (c)? Explain. Does the forecasting performance of
the model improve on that of any of the earlier models?
The analysis we carry out are all much, much easier in proper econometric software. In the text we have
used either EViews7 or PCGive.`
10.9 Durkin, Ord, and Walker (2010) examined the growth of credit markets in the United States since 1946.
The data file Credit.xlsx contains annual values for real mortgage credit (RMC), real consumer credit
(RCC), and real disposable personal income (RDPI) for the period 1946-2006. All the observations are
measured in billions of dol lars, after adjustment by the Consumer Price Index (CPI). Develop a VAR
model for these data for the period 1946-2003, and then forecast the last three years, 2004-2006. Examine
the relative advantages of a logarithmic transform and the use of differences.
10.10 Using the data set Gasprices_1.xlsx, but setting aside the data for 2006 through 2010, develop an
unrestricted VAR model, an ECM, and a model in stationary variables. Use appropriate error statistics to
examine the residuals and test their respective forecasting performances.
a. Do the residuals of the various models suggest any inadequacies in the model?
b. If you now consider the more recent data, from 2006 to 2010, does your chosen model show any
instability in its performance?
c. If you also bring into consideration the performance of the models over the years 2009-2010, which
model would you use for forecasting for the period 2011-2012? Explain your reasons.
WE use PcGive. Our focus is on explaining unleaded prices and our first model has included Unleaded,
CRUDE, CPI and Unemployment, with 3 lags. We will also take logs based on the analysis we carried out
in chapter 10. Use of PDI does not help the modelling although since it affects CPI it might prove of overall
benefits (some of the other factors might – perhaps we should extend the data base to include World Trade).
The forecasts for the last 5 years and the residuals are shown below.
A model with Unemployment and PDI was considered. From 2008 unemployment was persistently higher as
was PDI. The model was clearly inadequate.
Some programs including PCGive carry out automatic model selection. Here we summarize the results for
Log(Unleaded). Automatic model selection with insignificant lags excluded gives the following equation
for LogUnleaded
Graphs of the residuals and the forecasts compared to the actual are provided as shown:
Ord/Fildes Principles of Business Forecasting 1e Chapter 10 Exercises 10.7, 10.9, 10.10, 10.11 Solutions 2
All the variables show 2008-9 to generate large negative residuals caused by the major recession.
© 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted
in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
Ord/Fildes Principles of Business Forecasting 1e Chapter 10 Exercises 10.7, 10.9, 10.10, 10.11 Solutions 3
However, we’ve fitted an unconstained model. Is that the appropriate strategy? Checking using the ADF
(Dickey-Fuller) test we can establish the variables are not stationary – and a visual check and consideration
as to what they measure also confirms that conclusion.
We now fit the model to the log differenced data.
URF equation for: DlnUnlead
Coefficient Std.Error t-value t-prob
DlnUnlead_1 0.555595 0.1356 4.10 0.0001
DlnUnlead_2 -0.442501 0.1021 -4.34 0.0000
DlnCrude_1 0.194860 0.06470 3.01 0.0032
DlnCrude_3 0.161456 0.06010 2.69 0.0083
DCPI_1 -8.36960 2.912 -2.87 0.0049
Constant U 0.0191948 0.006881 2.79 0.0062
© 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted
in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
Ord/Fildes Principles of Business Forecasting 1e Chapter 10 Exercises 10.7, 10.9, 10.10, 10.11 Solutions 4
As before there is some limited evidence of outliers in 2009. The equation for: LUleaded
Coefficient Std.Error t-value t-prob
LUleaded_1 1.21294 0.1339 9.06 0.0000
LUleaded_2 -0.713818 0.1424 -5.01 0.0000
LUleaded_3 0.0696510 0.07329 0.950 0.3433
LCrude_1 0.241842 0.04189 5.77 0.0000
LCPI_1 -3.94918 2.479 -1.59 0.1131
LCPI_2 3.28624 2.387 1.38 0.1704
LPDI_1 0.438498 0.1657 2.65 0.0089
Constant U -1.17888 0.5739 -2.05 0.0415
The coefficients are somewhat similar apart from CPI. Note that both model estimations suggest that CPI should
be included in differenced form. It is of course a non-stationary variable as the graph makes clear.
© Using the most recent data, we first need to add in some dummy variables for the unexpected large impact of
the recession.
10.11* Using the data set Exchange_rates.xlsx, covering data on the $US-Euro and $US-£Sterling exchange
rates from June 13, 1991, to June 13, 2011,
a. Test the stationarity of each series
i. with the subset with data from October 13, 1997, to June 13, 2002.
ii. with the full data set.
b. For each time series, develop an ARIMA model that produces one-step-ahead daily forecasts. Then do
the same for monthly average exchange rates.
c. Are the two series cointegrated? Consider both the full and the shorter data sets.
d. Is there any evidence of structural breaks in the full data series?
© 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted
in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
Ord/Fildes Principles of Business Forecasting 1e Chapter 10 Exercises 10.7, 10.9, 10.10, 10.11 Solutions 5
e. Carry out a literature review of the comparative accuracy of alternative methods of exchange rate
forecasting. Do you find any evidence that any of the methods you have discovered have proved
successful beyond the random-walk naïve alternative?
© 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted
in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
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As Peter next undertook a journey to Leyden, the great scientist
Leeuwenhoek had to come on board his yacht. He brought some of
his most beautiful apparatus and a microscope with him. Peter
conversed with him for two hours, and manifested much pleasure in
the observation of the circulation of the blood in fishes. Boerhaave
took him to the Botanical Gardens and to the anatomical lecture-
room. On observing that one of his suite could not hide his aversion
for a body which seemed to him particularly worthy of observation
on account of its exposed sinews, he ordered him to tear out one of
these sinews with his teeth.
From Leyden, Peter returned to Amsterdam. Here he often joined
in the work on the galley which had been commenced at his request.
In the name of the town Vitsen requested the czar to accept this
ship as a present. Peter gave it the name Amsterdam, and in the
following year, laden with wares bought by Peter himself, it started
on its first journey to Archangel. From Amsterdam Peter often made
excursions to Zaandam, ever keen and confident, although his
Russian attendants trembled and quaked at the threatening dangers.
On market days he was greatly entertained by the quacks and tooth
drawers. He had one of the latter brought to him, and with great
dexterity soon acquired the knack necessary for this profession. His
servants had to provide him with opportunities for practising the
newly acquired art.
Through Vitsen the Dutch Jews petitioned the czar to permit their
nation, which had been banished by Ivan IV from Russia, to re-enter
it, and they offered to prove their gratitude by a present of 100,000
gulden. “My good Vitsen,” replied Peter, “you know my nation and
that it is not yet the time to grant the Jews this request. Tell them in
my name that I thank them for their offer, but that their condition
would become pitiable if they settled in Russia, for although they
have the reputation of swindling all the world in buying and selling, I
am afraid they would be greatly the losers by my Russians.”
During his sojourn in Amsterdam Peter received the joyful news of
two successful engagements against the Tatars in July and August.
To celebrate this victory he gave a brilliant fête to the authorities and
merchants of the town. The brilliant victory of Prince Eugene at
Zenta was yet more decisive for the issue of the war against the
Turks.
On the 9th of November Peter, accompanied only by Lefort,
returned to the Hague, where he informed King William III of his
desire to see England. The king preceded him, and sent three men
of war and a yacht under the command of Admiral Mitchel to
conduct the czar. On the 18th of January, 1698, accompanied by
Menshikov and fifteen other Russians of his suite, he set sail at
Hellevoetsluis. Soon after the first days of his arrival in England, he
exchanged the dwelling assigned to him in the royal castle of
Somerset for the house of Mr. Evelyn at Deptford in the
neighbourhood of the admiralty works, whence he could enter the
royal construction yards unseen. There he learned from the master
builders how to draw up the plan according to which a ship must be
built. He found extreme pleasure in observing the cannon at the
Tower, and also the mint, which then excelled all others in the art of
stamping.
In his honour Admiral Carmarthen instituted a sham sea fight at
Spithead on the 3rd of April which was conducted on a greater scale
than a similar spectacle given for him in Holland. He often visited the
great cathedrals and churches. He paid great attention to the
ceremonial of English church worship; he also visited the meeting-
houses of the Quakers and other sects. At Oxford he had the
organisation and institutions of the university shown him. As in
Holland, he preferred to pass most of his time with handicraftsmen
and artists of every kind; from the watchmaker to the coffin maker,
all had to show him their work, and he took models with him to
Russia of all the best and newest. During his stay he always dressed
either as an English gentleman or in a naval uniform.
In Holland the English merchants had presented the czar with a
memorial through Count Pembroke on the 3rd of November, 1697, in
which they had petitioned for permission to import tobacco (which
had been so strongly forbidden under the czars Michael and Alexis),
and offered to pay a considerable sum of money for the privilege.
The marquis of Carmarthen now again broached the subject, and on
the 16th of April a treaty was signed with the Russian ambassador
Golovin for three years, which authorised Carmarthen’s agents to
import into the Russian Empire in the first year three thousand
hogsheads (of five hundred English pounds each), and in each of the
following two years four thousand hogsheads, against a tax of 4
kopecks in the pound. Twelve thousand pounds were paid down in
advance. This money placed the czar in a position to make still
greater purchases, as well as to engage a greater number of
foreigners in his service; amongst them the astronomer and
professor of mathematics Ferguson of Scotland, the engineer
Captain Perry, and the shipbuilders John Dean and Joseph Ney.f
King William made Peter a present of the
[1698 a.d.] Royal Transport, a very beautiful yacht, which
he generally used for his passage over to
Holland. Peter went on board this vessel, and got back to Holland in
the end of May, 1698. He took with him three captains of men-of-
war, five-and-twenty captains of merchant ships, forty lieutenants,
thirty pilots, thirty surgeons, two hundred and fifty gunners, and
upwards of three hundred artificers. This colony of ingenious men in
the several arts and professions sailed from Holland to Archangel on
board the Royal Transport; and were sent thence to the different
places where their service was necessary. Those whom he engaged
at Amsterdam took the route of Narva, at that time subject to
Sweden.
While the czar was thus transporting the arts and manufactures
from England and Holland to his own dominions, the officers whom
he had sent to Rome and Italy succeeded so far as also to engage
some artists in his service. General Sheremetrev, who was at the
head of his embassy to Italy, made the tour of Rome, Naples,
Venice, and Malta; while the czar proceeded to Vienna with the other
ambassadors. All he had to do now was to observe the military
discipline of the Germans, after seeing the English fleet and the
dockyards in Holland. But it was not the desire of improvement alone
that induced him to make this tour to Vienna, he had likewise a
political view; for the emperor of Germany was the natural ally of
the Russians against the Turks. Peter had a private audience of
Leopold, and the two monarchs stood the whole time of the
interview, to avoid the trouble of ceremony.
EXECUTION OF THE STRELITZ BY COMMAND OF PETER THE
GREAT
While Charles was engaged in Poland, Peter gained time for the
accomplishment of those measures which his situation suggested.
Despatching a body of troops to protect the frontiers at Pskov, he
repaired in person to Moscow, and occupied himself throughout the
ensuing winter in raising and training six regiments of infantry,
consisting of 1000 men each, and several regiments of dragoons.
Having lost 145 pieces of cannon in the affair at Narva he ordered a
certain proportion of the bells of the convents and churches to be
cast into field pieces; and was prepared in the spring of the year
1701 to resume hostilities with increased strength, and an artillery of
100 pieces of cannon, 142 field pieces, 12 mortars, and 13
howitzers.
Nor did he confine his attention to the improvement of the army.
Conscious of the importance of diffusing employment amongst his
subjects, and increasing their domestic prosperity, he introduced into
the country flocks of sheep from Saxony, and shepherds to attend to
them, for the sake of the wool; established hospitals, and linen and
paper manufactories; encouraged the art of printing; and invited
from distant places a variety of artisans to impart to the lower
classes a knowledge of useful crafts. These proceedings were
treated with levity and contempt by Charles, who appears all
throughout to have despised the Russians, and who, engrossed by
his campaign in Courland and Lithuania, intended to turn back to
Moscow at his leisure, after he should have dethroned Augustus, and
ravaged the domains of Saxony.
Unfortunately the divisions that prevailed in the councils of Poland
assisted to carry these projects rapidly into effect. Peter was anxious
to enter into a new alliance with Augustus, but, in an interview he
held with that prince at Birzen, he discovered the weakness of his
position and the hopelessness of expecting any effectual succour at
his hands. The Polish diet, equally jealous of the interference of the
Saxon and Russian soldiery in their affairs, and afraid to incur the
hostility of Charles, refused to sanction a league that threatened to
involve them in serious difficulties. Hence, Augustus, left to his own
resources, was easily deprived of a throne which he seemed to hold
against the consent of the people, while Peter was forced to conduct
the war alone. His measures were consequently taken with
promptitude and decision. His army was no sooner prepared for
action than he re-entered Ingria, animating the troops by his
presence at the several points to which he directed their
movements. In some accidental skirmishes with small bodies of the
Swedes, he reaped a series of minor successes, that inspired the
soldiers with confidence and improved their skill for the more
important scenes that were to follow. Constantly in motion between
Pskov, Moscow, and Archangel, at which last place he built a fortress
called the New Dvina, he diffused a spirit of enthusiasm amongst the
soldiers, who were now becoming inured to action.
An open battle at last took place in the
[1702 a.d.] neighbourhood of Dorpat, on the borders of
Livonia, when General Sheremetrev fell in with
the main body of the enemy on the 1st of January, 1702, and, after
a severe conflict of four hours, compelled them to abandon their
artillery and fly in disorder. On this occasion, the Swedes are said to
have lost three thousand men, while there were but one thousand
killed on the opposite side. General Sheremetrev was immediately
created a field-marshal, and public thanks were offered up for the
victory.
Following up this signal triumph, the czar equipped one fleet upon
Lake Peipus to protect the territory of Novgorod, and manned
another upon Lake Ladoga, to resist the Swedes in case they should
attempt a landing. Thus guarded at the vulnerable points, he was
enabled to prosecute his plans in the interior with greater certainty
and effect.
Marshal Sheremetrev in the meantime marched upon Marienburg,
a town on the confines of Livonia and Ingria, achieving on his
progress another triumph over the enemy near the village of
Humolova. The garrison at Marienburg, afraid to risk the
consequences of a siege, capitulated at once, on condition that the
inhabitants should be permitted a free passage, which was agreed
to; but an intemperate officer having set fire to the powder
magazine, to prevent the negotiation from being effected, by which
a number of soldiers on both sides were killed, the Russians fell
upon the inhabitants and destroyed the town.
RENEWED HOSTILITIES
POLISH AFFAIRS