Time Series Modeling

 

Time series are particularly useful to track variables such as revenues, costs, and profits over time. Time series models help evaluate performance and make predictions. Consider the following and respond in a minimum of 175 words:

Time series decomposition seeks to separate the time series (Y) into 4 components: trend (T), cycle (C), seasonal (S), and irregular (I). What is the difference between these components?
The model can be additive or multiplicative. When we do use an additive model? When do we use a multiplicative model?
The following list gives the gross federal debt(in millions of dollars) for the U.S. every 5 years from 1945 to 2000:
Year Gross Federal Debt ($millions)

1945 260,123

1950 256,853

1955 274,366

1960 290,525

1965 322,318

1970 380,921

1975 541,925

1980 909,050

1985 1,817,521

1990 3,206,564

1995 4,921,005

2000 5,686,338

Construct a scatter plot with this data. Do you observe a trend? If so, what type of trend do you observe?
Use Excel to fit a linear trend and an exponential trend into the data. Display the models and their respective r^2.
Interpret both models. Which model seems to be more appropriate? Why?

Sample Solution

up with a hypothesis, alongside pioneers today including Frowe (2011). Their hypothesis is formulated as an aide, regardless of whether we ought to do battle alongside conditions which should be thought of, how would it be a good idea for us we respond and not do during a conflict in the event that it is unavoidable, lastly what further move ought to be made later. To assess this hypothesis, one should take a gander at the suspicions made towards it, for instance, entertainers which scholars forget about and the delay between conventional scholars and innovators. In particular, there can be no conclusive hypothesis of the simply war, in light of the fact that everyone has an alternate understanding of this hypothesis, given its normativity. In any case, the hypothesis gives a harsh presentation of how we ought to continue in the midst of pressure and struggle, essentially the point of a simply war: ‘harmony and security of the district’ (Begby et al, 2006b, Page 310). Generally, this hypothesis is reasonable to utilize yet can’t at any point be viewed as a characteristic aide since it’s normatively conjectured. To respond to the inquiry, the exposition is involved 3 segments.

Jus promotion bellum
The beginning segment covers jus promotion bellum, the circumstances discussing whether an activity is legitimately OK to cause a conflict (Frowe (2011), Page 50). Vittola, first and foremost, examines one of the worthwhile motivations of war, in particular, is when damage is caused however he causes notice the damage doesn’t prompt conflict, it relies upon the degree or proportionality, one more condition to jus promotion bellum (Begby et al (2006b), Page 314). Frowe, nonetheless, contends the possibility of “worthy motivation” in light of “Power” which alludes to the security of political and regional privileges, alongside common freedoms. In contemporary view, this view is more convoluted to reply, given the ascent of globalization. Essentially, it is hard to gauge proportionality, especially in war, in light of the fact that not just that there is an epistemic issue in working out, yet again the present world has created (Frowe (2011), Page 54-6). Besides, Vittola contends war is fundamental, not just for protective purposes, ‘since it is legal to oppose force with force,’ yet in addition to battle against the treacherous, a hostile conflict, countries which are not rebuffed for acting unreasonably towards its own kin or have shamefully taken land from the home country (Begby et al (2006b), Page 310&313); to “show its foes a thing or two,” yet principally to accomplish the point of war. This approves Aristotle’s contention: ‘there should be battle for harmony (Aristotle (1996), Page 187). Nonetheless, Frowe contends “self-preservation” has a majority of portrayals, found in Part 1, demonstrating the way that self-protection can’t necessarily legitimize one’s activities. Much more risky, is the situation of self-protection in war, where two clashing perspectives are laid out: The Collectivists, a totally different hypothesis and the Individualists, the continuation of the homegrown hypothesis of self-preservation (Frowe (2011), Page 9& 29-34). All the more critically, Frowe discredits Vittola’s view on retribution in light of the fact that right off the bat it enables the punisher’s power, yet additionally the present world forestalls this activity between nations through lawful bodies like the UN, since we have modernized into a generally tranquil society (Frowe (2011), Page 80-1). Above all, Frowe further disproves Vittola through his case that ‘right goal can’t be blamed so as to take up arms in light of expected wrong,’ recommending we can’t simply hurt another in light of the fact that they have accomplished something unfair. Different elements should be thought of, for instance, Proportionality. Thirdly, Vittola contends that war ought to be stayed away from (Begby et al (2006b), Page 332) and that we ought to continue conditions carefully. This is upheld by the “final retreat” position in Frowe, where war ought not be allowed except if all actions to look for strategy falls flat (Frowe (2011), Page 62). This implies war ought not be pronounced until one party must choose the option to proclaim battle, to safeguard

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