Holt exponential smoothing modelling Simple exponential smoothing does not do well when there is a trend in the data, which is inconvenient. In such situations, several methods were devised under the name "double exponential smoothing" or "second-order exponential smoothing", which is the recursive application of an exponential filter twice, thus being termed "double exponential smoothing". This nomenclature is similar to quadruple exponential smoothing, which also references its recursion depth. The basic idea behind double exponential smoothing is to introduce a term to take into account the possibility of a series exhibiting some form of trend. This slope component is itself updated via exponential smoothing. Holt exponential smoothing …show more content…
In a series with a linear trend, this should equal the slope of the trend with some added noise specific for the situation at the time index t. The trend slop, which is allowed to be time varying, is denoted b_t. The idea is basically to update the true level using the present observation X_t from the previous level X ̃_(t-1) to X ̃_t by an adjustment to the previous slope element b_(t-1) using exponential smoothing. Moreover, the basic formula for exponential smoothing is applied to update from the estimate of b_(t-1) to an estimate of actual b_t as anaverage of last slop element b_(t-1) and the present observed incrementX ̃_t-X ̃_(t-1) of the estimated true level. Expressed as formulas, these two updating equations then …show more content…
Air-quality indices: elaboration, uses and international comparisons. Presses des MINES. [2]"People's Republic of China Ministry of Environmental Protection Standard: Technical Regulation on Ambient Air Quality Index". Access:http://kjs.mep.gov.cn/hjbhbz/bzwb/dqhjbh/jcgfffbz/201203/W020120410332725219541.pdf [3] Box, G.E.P., Jenkins, G.M., and Reinsel, G.C.(1994), Time Series Analysis: Forecasting and Control, 3rd edition, Prentice Hall: Englewood Cliffs, New Jersey. [4] Anders Milhoj (2013). Practical Time Series Analysis Using SAS. NC: SAS Institute Inc, Cary. [5] SAS Institute Inc, (2014). SAS/STAT® 9.4 User’s Guide: The ESM Procedure (Book Excerpt). NC: SAS Institute Inc, Cary. [6] Bollerslev T. Generalized autoregressive conditionalheteroskedasticity [J]. Journal of Econometrics, 1986, 31 (3):309-317. [7] Engle R.F. Autoregressive conditional heteroskedasticity withestimates of the variance of United Kingdom inflation [J].Econometric, 1982, 50 (4): 989-1004. [8] Engle R.F., Kroner F.K. Multivariate SimultaneousGeneralized ARCH [J].Econometric Theory, 1995,
Clark, Todd and Christian Garciga. "Recent Inflation Trends." Economic Trends (07482922), 14 Jan. 2016, pp. 5-11. EBSCOhost, cco.idm.oclc.org/login?url=http://search.ebscohost.com/login.aspx?direct=true&db=aph&AN=112325646&site=ehost-live.
J. Scott Armstrong and Fred Collopy, “Error Measures For Generalizing About Forecasting Methods: Empirical Comparisons”. International Journal of Forecasting, Vol. 8, pp. 69–80, 1992.
A trend analysis of the unemployment rates, inflation, nominal GDP, and real GDP were tabulated and graphed as shown below. From the graphs, it is evident that inflation and unemployment rates have a non-deterministic curve and fluctuate over time. The progression occurs because inflation and unemployment can be caused by many other factors apart from the economic growth (Mankiw 58). For instance, changes in international market prices, advancements in technology, and the use of different methods of production.
There are three different general trends (directions to prices or rates) in the economy. " Those with predictive value are leading indicators; those occurring at the same time as the related economic activity are coincident indicators; and those that only become apparent after the activity are lagging indicators. Examples are unemployment, housing starts, Consumer Price Index, industrial production, bankruptcies, GDP, stock market prices, money supply changes, and housing starts also called business indicators." http://www.investorwords.com/1643/economic_indicator.html.
Knoop, A, T, 2011, Recessions and depressions: understanding business cycles, ABC-CLIO, United States of America
Please go through and write the part for the modeling. (preliminary data and aim 4).
An economic indicator is a statistic of the current status of the economy. This can predict how the economy may perform in the future. Investors and other private or government organizations use this information as a tool to make business decisions. By gathering historical data about the economy and comparing it to current trends, one can compile a snapshot of economic fluctuations. The direction of an indicator may vary according to changes in the economy. The indicator can be leading, lagging, or coincident. Leading indicators are changes before the economy has recognized the changed. Lagging indicators do not change until a few quarters after the economy has change. Coincident indicators move at the same time as the economy (The Library of Congress, 2005). Some of the common indicators are GDP, Unemployment Rate, Inflation Rate, Capacity utilization, Auto sales, and Personal income. As the explanation of these six indicators will be use to forecast the future of the economy, the trend of these indicators will also be used to evaluate the economy's historical and future outcome.
The next model is the Quadratic Trend Model. The quadratic formula uses the least-squares method to forecast and can be written as Yi =b_0+ b_1 X_1+ b_2 X_2. In this formula the only difference is b_2 X_2 represents the estimated quadratic effect on Y. Figure 1-6 represents the comparison between the linear and quadratic
Inflation; ‘a situation in which prices rise in order to keep up with increased production costs… result[ing] [in] the purchasing power of money fall[ing]’ (Collin:101) is quickly becoming a problem for the government of the United Kingdom in these post-recession years. The economic recovery, essential to the wellbeing of the British economy, may be in jeopardy as inflation continues to rise, reducing the purchasing power of the public. This, in turn, reduces demand for goods and services, and could potentially plummet the UK back into recession. This essay discusses the causes of inflation, policy options available to the UK government and the Bank of England (the central bank of the UK responsible for monetary policy), and the effects they may potentially have on the UK recovery.
The revised United States Environmental Protection Agency National Ambient Air Quality Standards (US EPA NAAQS) for Particulate matter PM2.5 and other air pollutants could be exceeded not only outdoors but also indoors. This is based on the different studies on indoor and outdoor particulate matter in the inner-city environment or even in the neighborhood of busy major roads.
The purpose of this paper is to explain the advances being made in technology and algorithms in helping advance the accuracy of forecasting. It will contrast the forecasting methods of several decades ago with forecasting methods in use today. In discussing how errors can accumulate over time and providing simple mathematical formulas as examples, this paper intends to show how the repetition of minor errors can affect the accuracy of weather predictions.
Many cities are currently affected by air pollution and Hong Kong is one example. Hong Kong’s air pollution level often exceeds the recommended air pollution level put out by the World Health Organization, and Hong Kong’s pollution index was at “very high” meaning that it exceeded 101, for 34% of the time (Hunt, 2011). Another example, when Hong Kong excee...
Wong, Edward. "Most Chinese Cities Fail Minimum Air Quality Standards, Study Says." The New York Times. The New York Times, 27 Mar. 2014. Web. 10 Apr. 2014.
Abstract- The control limits for exponentially weighted moving average (EWMA) varies with time and approaches_asymptotic limit as the time passes. The shift detection is measured by how much the process goes out of the control limits. The shift is auto corrected by using the variable chart for subgroups. The main assumption behind the Principal Component Analysis (PCA) is discussed and comparisons are made between the multivariate EWMA used in PCA to other methods of statistical control processes.
Archdeacon, T. J. (1994). Correlation and regression analysis: A historian's guide. Madison, Wis: University of Wisconsin Press.