Kz2418571860

Nageswara Rao Puli, Nagul Shaik, M.Kishore Kumar / International Journal of Engineering
Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue4, July-August 2012, pp.1857-1860
A New Generic Architecture For Time Series Prediction

*Nageswara Rao Puli, **Nagul Shaik,***M.Kishore Kumar
*Dept. of Computer Science & Engg
Nimra Institute of Science and Technology
Vijayawada, India
**Asst.Professor, Dept. of Computer Science & Engg
Vijayawada, India
***Professor & HOD Dept. of Computer Science & Engg
Vijayawada, India

Abstract
Rapidly evolving businesses generate xt 1 , xt 2 , data values. The goal is to observe or
massive amounts of time-stamped data sequences
model the existing data series to enable future
and cause a demand for both univari- ate and
unknown data values to be forecasted accurately.
multivariate time series forecasting. For such data,
Examples of data series include financial data series
traditional predictive models based on
(stocks, indices, rates, etc.), physically observed data
autoregression are often not sufficient to capture
series (sunspots, weather, etc.), and mathematical
complex non-linear relationships between
data series (Fibonacci sequence, integrals of
multidimensional fea- tures and the time series
differential equations, etc.). The phrase “time series”
outputs. In order to exploit these relationships for
generically refers to any data series, whether or not
improved time series forecasting while also better
the data are dependent on a certain time increment.
dealing with a wider variety of prediction
Throughout the literature, many techniques have been
scenarios, a forecasting system requires a ﬂexible
implemented to perform time series forecasting. This
and generic architecture to accommodate and tune
paper will focus on two techniques: neural networks
various individual predictors as well as
and k-nearest-neighbor. This paper will attempt to
combination methods.
fill a gap in the abundant neural network time series
In reply to this challenge, an architecture
forecasting literature, where testing arbitrary neural
for combined, multilevel time series prediction is
networks on arbitrarily complex data series is
proposed, which is suitable for many different
common, but not very enlightening. This paper
universal regressors and combination methods. The
thoroughly analyzes the responses of specific neural
key strength of this architecture is its ability to
network configurations to artificial data series, where
build a diversified ensemble of individual
each data series has a specific characteristic. A better
predictors that form the input to a multilevel
understanding of what causes the basic neural
selection and fusion process before the final
network to become an inadequate forecasting
optimised output is obtained. Excellent
technique will be gained. In addition, the influence
generalisation ability is achieved due to the highly
of data preprocessing will be noted. The forecasting
boosted complementarity of individual models
performance of k-nearest-neighbor, which is a much
further enforced through crossvalidation-linked
simpler forecasting technique, will be compared to
training on exclusive data subsets and ensemble
the neural networks’ performance. Finally, both
output post-processing. In a sample configuration
techniques will be used to forecast a real data series.
with basic neural network predictors and a mean
combiner, the proposed system has been evaluated
in different scenarios and showed a clear prediction Difficulties
performance gain. Several difficulties can arise when
performing time series forecasting. Depending on the
type of data series, a particular difficulty may or may
Index Terms— Time series forecasting, combining
not exist. A first difficulty is a limited quantity of
predictors, regression, ensembles, neural networks,
data. With data series that are observed, limited data
diversity
may be the foremost difficulty. For example, given a
company’s stock that has been publicly traded for one
Introduction year, a very limited amount of data are available for
Time series forecasting, or time series use by the forecasting technique.
prediction, takes an existing series of data
xt n , , xt 2 , xt 1 , xt and forecasts the
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A second difficulty is noise. Two types of data series.Another application is forecasting
noisy data are (1) erroneous data points and (2) undesirable, yet unavoidable, events to preemptively
components that obscure the underlying form of the lessen their impact. At the time of this writing, the
data series. Two examples of erroneous data are sun’s cycle of storms, called solar maximum, is of
measurement errors and a change in measurement concern because the storms cause technological
methods or metrics. In this paper, we will not be disruptions on Earth. The sunspots data series, which
concerned about erroneous data points. An example is data counting dark patches on the sun and is related
of a component that obscures the underlying form of to the solar storms, shows an eleven-year cycle of
the data series is an additive high-frequency solar maximum activity, and if accurately modeled,
component. The technique used in this paper to can forecast the severity of future activity. While
reduce or remove this type of noise is the moving solar activity is unavoidable, its impact can be
average. The data series , xt 4 , xt 3 , xt 2 , xt 1 , xt lessened with appropriate forecasting and proactive
action.
becomes
Finally, many people, primarily in the
, ( xt4  xt3  xt2 ) / 3, ( xt3  xt2  xt1 ) / 3, ( xt2  xt1  xt ) / 3 financial markets, would like to profit from time
after taking a moving average with an interval i of series forecasting. Whether this is viable is most
three. Taking a moving average reduces the number likely a never-to-be-resolved question. Nevertheless
of data points in the series by i  1 . many products are available for financial forecasting.
A third difficulty is nonstationarity, data that Difficulties inherent in time series forecasting and the
do not have the same statistical properties (e.g., mean importance of time series forecasting are presented
and variance) at each point in time. A simple next. Then, neural networks and k-nearest-neighbor
example of a nonstationary series is the Fibonacci are detailed. Section Error! Reference source not
sequence: at every step the sequence takes on a new, found. presents related work. Section Error!
higher mean value. The technique used in this paper Reference source not found. gives an application
to make a series stationary in the mean is first- level description of the test-bed application, and
Section Error! Reference source not found.
differencing. The data series , xt 3 , xt 2 , xt 1 , xt presents an empirical evaluation of the results
becomes obtained with the application.A time series is a
, ( xt 2  xt 3 ), ( xt 1  xt 2 ), ( xt  xt 1 ) after sequence of observations of a random variable.
Hence, it is a stochasticprocess. Examples include the
taking the first-difference. This usually makes a data
monthly demand for a product, the annual
series stationary in the mean. If not, the second-
freshmanenrollment in a department of a university,
difference of the series can be taken. Taking the first-
and the daily volume of flows in a river.Forecasting
difference reduces the number of data points in the
time series data is important component of operations
series by one.
research because thesedata often provide the
A fourth difficulty is forecasting technique
foundation for decision models. An inventory model
selection. From statistics to artificial intelligence,
requiresestimates of future demands, a course
there are myriad choices of techniques. One of the
scheduling and staffing model for a universityrequires
simplest techniques is to search a data series for
estimates of future student inflow, and a model for
similar past events and use the matches to make a
providing warnings to thepopulation in a river basin
forecast. One of the most complex techniques is to
requires estimates of river flows for the immediate
train a model on the series and use the model to make
future.Time series analysis provides tools for
a forecast. K-nearest-neighbor and neural networks
selecting a model that can be used to forecastof future
are examples of the first and second techniques,
events. Modeling the time series is a statistical
respectively.
problem. Forecasts are used incomputational
procedures to estimate the parameters of a model
1) Importance
being used to allocatedlimited resources or to
Time series forecasting has several
describe random processes such as those mentioned
important applications. One application is preventing
above. Timeseries models assume that observations
undesirable events by forecasting the event,
vary according to some probability distributionabout
identifying the circumstances preceding the event,
an underlying function of time.styles are built-in;
and taking corrective action so the event can be
examples of the type styles are provided throughout
avoided. At the time of this writing, the Federal
this document and are identified in italic type, within
Reserve Committee is actively raising interest rates to
parentheses, following the example. PLEASE DO
head off a possible inflationary economic period.
NOT RE-ADJUST THESE MARGINS.
The Committee possibly uses time series forecasting
with many data series to forecast the inflationary
period and then acts to alter the future values of the

1858 | P a g e

. Each output layer unit performs the calculation in
In this section and the next, subscripts c, p, Equation II.1 on its inputs and transfers the result
and n will identify units in the current layer, the (Oc) to a network output.
previous layer, and the next layer, respectively.
Equation II.1 Activation function of an output layer
When the network is run, each hidden layer unit
unit.
performs the calculation in Error! Reference source
Each output layer unit performs the calculation in
not found. on its inputs and transfers the result (Oc)
Equation II.1 on its inputs and transfers the result
to the next layer of units.
(Oc) to a network output.
Equation II.2 Activation function of an output layer
unit.

P 
Oc  hOutput  ic , p wc , p  bc  where hOutput( x )  x
 p1 
Oc is the output of the current output layer
unit c, P is the number of units in the previous
P  1
Oc  hHidden   ic , p wc , p  bc  where hHidden ( x )  hidden layer, ic,p is an input to unit c from the
 p1  1  ex
previous hidden layer unit p, wc,p is the weight
modifying the connection from unit p to unit c, and
Fig: Forwarding the node values bc is the bias. For this research, hOutput(x) is a
linear activation function1
Oc is the output of the current hidden layer unit c, P is
K-Nearest-Neighbor
In contrast to the complexity of the neural
either the number of units in the previous hidden network forecasting technique, the simpler k-nearest-
layer or number of network inputs, ic,p is an input to neighbor forecasting technique is also implemented
unit c from either the previous hidden layer unit p or and tested. K-nearest-neighbor is simpler because
network input p, wc,p is the weight modifying the there is no model to train on the data series. Instead,
connection from either unit p to unit c or from input p the data series is searched for situations similar to the
to unit c, and bc is the bias. current one each time a forecast needs to be made.
In Error! Reference source not found., hHidden(x) is To make the k-nearest-neighbor process description
easier, several terms will be defined. The final data
points of the data series are the reference, and the
length of the reference is the window size. The data
series without the last data point is the shortened data
series. To forecast the data series’ next data point,
the reference is compared to the first group of data
points in the shortened data series, called a candidate,
and an error is computed. Then the reference is
moved one data point forward to the next candidate
the sigmoid activation function of the unit and is and another error is computed, and so on. All errors
charted in Error! Reference source not found.. are stored and sorted. The smallest k errors
correspond to the k candidates that closest match the
Fig: Nearest Neighbor Transformation
Fig: Prediction Graph for Forwarding node

Other types of activation functions exist, but the
sigmoid was implemented for this research. To avoid
saturating the activation function, which makes
training the network difficult, the training data must
be scaled appropriately. Similarly, before training, the
weights and biases are initialized to appropriately
scaled values. reference. Finally, the forecast will be the
average of the k data points that follow these
candidates. Then, to forecast the next data point, the

1859 | P a g e

process is repeated with the previously forecasted data [4]. Hebb, D. O. (1949). The Organization of
point appended to the end of the data series. Behavior: A Neuropsychological Theory.
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II. CONCLUSION [5]. Kingdon, J. (1997). Intelligent Systems and
Section Error! Reference source not found. Financial Forecasting. New York: Springer-
introduced time series forecasting, described the work Verlag.
presented in the typical neural network paper, which [6]. Lawrence, S., Tsoi, A. C., & Giles, C. L.
justified this paper, and identified several difficulties (1996). Noisy Time Series Prediction Using
associated with time series forecasting. Among these Symbolic Representation and Recurrent
difficulties, noisy and nonstationary data were Neural Network Grammatical Inference
investigated further in this paper. Section Error! [Online]. Available:
Reference source not found. also presented feed- http://www.neci.nj.nec.com/homepages/lawr
forward neural networks and backpropagation ence/papers/finance-tr96/latex.html [March
training, which was used as the primary time series 27, 2000].
forecasting technique in this paper. Finally, k-nearest- [7]. McCulloch, W. S., & Pitts, W. H. (1943). A
neighbor was presented as an alternative forecasting Logical Calculus of the Ideas Imminent in
technique. Nervous Activity. Bulletin of Mathematical
Section Error! Reference source not found. briefly Biophysics, 5, 115-133.
discussed previous time series forecasting papers. The [8]. Minsky, M., & Papert, S. (1969).
most notable of these being the paper by Drossu and Perceptrons: An Introduction to
Obradovic (1996), who presented compelling research Computational Geometry. Cambridge, MA:
combining stochastic techniques and neural networks. MIT Press.
Also of interest were the paper by Geva (1998) and [9]. Rosenblatt, F. (1962). Principles of
the book by Kingdon (1997), which took significantly Neurodynamics: Perceptrons and the Theory
more sophisticated approaches to time series of Brain Mechanisms. Washington, D. C.:
forecasting. Spartan.
Section Error! Reference source not found. [10]. Rumelhart, D. E., Hinton, G. E., &
presented Forecaster and went through several Williams, R. J. (1986). Learning Internal
important aspects of its design, including parsing data Representations by Error Propagation. In D.
files, using the Wizard to create networks, training E. Rumelhart, et al. (Eds.), Parallel
networks, and forecasting using neural networks and Distributed Processing: Explorations in the
k-nearest-neighbor. Microstructures of Cognition, 1:
Section Error! Reference source not found. Foundations, 318-362. Cambridge, MA:
presented the crux of the paper. First, the data series MIT Press.
used in the evaluation were described, and then [11]. Torrence, C., & Compo, G. P. (1998). A
parameters and procedures used in forecasting were Practical Guide to Wavelet Analysis
given. Among these was a method for selecting the [Online]. Bulletin of the American
number of neural network inputs based on data series Meteorological Society. Available:
characteristics (also applicable to selecting the http://paos.colorado.edu/research/wavelets/
window size for k-nearest-neighbor), a training [July 2, 2000].
heuristic, and a metric for making quantitative forecast [12]. Zhang, X., & Thearling, K. (1994). Non-
comparisons. Finally, a variety of charts and tables, Linear Time-Series Prediction by Systematic
accompanied by many empirical observations, were Data Exploration on a Massively Parallel
presented for networks trained heuristically and Computer [Online]. Available:
simply and for k-nearest-neighbor. http://www3.shore.net/~kht/text/sfitr/sfitr.ht
m [March 27, 2000].
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[1]. Drossu, R., & Obradovic, Z. (1996). Rapid
Design of Neural Networks for Time Series
Prediction. IEEE Computational Science &
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[2]. Geva, A. (1998). ScaleNet—Multiscale
Neural-Network Architecture for Time
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Neural Networks, 9(5), 1471-1482.
[3]. Gonzalez, R. C. & Woods, R. E. (1993).
Digital Image Processing. New York:
Addison-Wesley.

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