Farnum, N.R. and Stanton, L.W." : Quantitative Forecasting Methods. PWS-Kent Publishing Company, 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....data available. Secondly, some of models mentioned above, e.g. HoltWinters smoothing, Regression method, and Time series method, are applicable for the specified situation where data distribution characterized the wave form with regular variation or normally distributed for a certain system [4][7], for example, the seasonal or cyclical data series. Contrarily, the GM(1,1 a) model introduced in [8] just need a few data for model construction implied the simple and reasonable prediction accuracy. Thus, the GM(1,1 a) model is often utilized in the short term forecast for years. Although the ....

....T a T a T a a n X X X X ) 2 , k a i x i x i x i X ) 1 [ 2 k y y y Y ) 2 ( 1 ( k b b b b B ] 2 1 0 = Step 2: Derived the normal equation to find pseudo inverse matrix Solving for Eq. 10) typically turns out to be a normal equation [7], Y X B X X a a T a = 11) in which matrix B is a coefficient vector for k b b b , 1 0 in Eq. 8) and Y is observed values given by in Eq. 8) Step 3: Solving the appropriate coefficients and Predicting the next output The solution to B in the normal equation is equal to Y X a a X ....

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N. R. Farnum and L. W. Stanton, Quantitative Forecasting Method, Boston: PWS-KENT, 1989.

....2m 1 Then, normali q= R , z = R R #R we reject H 0 i z z # 2 . Where # i the confidence level of the test. For m # 20,R cannot be consi( q= as normallydiallyq) 6 sia i i anasymptoti property. However, confidencei tervals [R L,R U ] for small samplesipl can also be calculated. In [3], a tablei provi7R for values of m # 20 and # =0.10. We have reproducedi i Tab. 1. m 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 RL 2334567789101111121314 RU 10 11 13 14 15 16 17 17 19 20 22 23 25 26 27 28 Tab. 1:Cri) values forR i a two tai7q runs test for stati(q=77 y (# =0.10) If H 0i ....

N.R. Farnum and L.W. Stanton. Quantitative Forecasting Methods. PWS-Kent Publi"6q= Company, 1989. 11

....of individual customers so as to recognize superimposed fraudulent behavior. Mining the data to derive profiling features is not necessary. Because fraud happens over time, methods that deal with time series are relevant to this work. However, traditional time series analysis (Chatfield 1984; Farnum and Stanton 1989) in statistics strives either to characterize an entire time series or to forecast future events in the series. Neither ability is directly useful to fraud detection. Hidden Markov Models (Rabiner and Juang 1986; Smyth 1994) are concerned with distinguishing recurring sequences of states and the ....

Farnum, N. and L. Stanton (1989). Quantitative forecasting methods. Boston, MA: PWS-Kent Publishing Company.

....normally distributed and that underlying correlations are linear. As it will be shown in x2.5 this assumption can not always be made. Stationarity Transformations Once a time series is found to be non stationary it is usually transformed by either differencing or calculation of link relatives (Farnum and Stanton 1989). Differencing a series with a linear trend would result in a no trend series; if a trend is quadratic then second differences may be needed. This process has two main disadvantages: with each differencing a data point is lost (which is important in short time series) and more importantly, ....

....and decisions are made regarding the importance and the meaning of the results. Depending on the analyst s preferences and results of various tests a forecasting method is selected and fitted to the data. Fig. 2.3. 1 shows one possible method flowchart for selection of forecasting methods, after (Farnum and Stanton 1989). No Yes No Yes No Transform Data for Stationarity Examine: 2. ACF of Series 1. Graph of Series ARIMA Data with Trend Seasonality Autocorrelated Errors Wish to Transform Start MA, ES . SSES, AHW, MHW . DMA, DES, LES . Pass Statistical Tests Figure 2.3.1: Example model selection ....

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Farnum, N. R. and L. W. Stanton (1989). Quantitative Forecasting Methods. Boston: PWS-KENT Publishing.

....is not necessary. Ezawa and Norton s method of evidence combining is much more sophisticated than ours and faces some of the same problems (unequal error costs, skewed class distributions) Methods that deal with time series are relevant to our work. However, time series analysis (Chatfield 1984; Farnum Stanton 1989) strives to characterize an entire time series or to forecast future events in the series. Neither ability is directly useful to fraud detection. Hidden Markov Models (Rabiner Juang 1986) are concerned with distinguishing recurring sequences of states and the transitions between them. However, ....

Farnum, N., and Stanton, L. 1989. Quantitative forecasting methods. Boston, MA: PWS-Kent Publishing Company.

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Farnum, N.R. and Stanton, L.W." : Quantitative Forecasting Methods. PWS-Kent Publishing Company, 1989.

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N.R. Farnum and L.W. Stanton. Quantitative Forecasting Methods. PWS-Kent Publi"6q= Company, 1989. 11

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