Which of the following is not a necessary condition for weakly stationary time series

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2020. 1. 11. · What’s Next. This is just the first step in time series analysis. For the majority of algorithms, the series must be stationary, in order for the analysis and predictions to be performed. That’s the main reason why I think this step needs to be automated — it’s tedious to test many differentiation orders manually.. Now you have the tools to proceed.

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We discuss the moment condition for the fractional functional central limit theorem (FCLT) for partial sums of x t = Δ − d u t, where is the fractional integration parameter and u t is weakly dependent. The classical condition is existence of q ≥ 2 and moments of the innovation sequence. When d is close to this moment condition is very strong. Our main result is to show that when and.

2019. 12. 17. · By Exponential rate, we mean growth at a constant rate with continuous compounding. This can be seen as follows: Using the time series formula above, the value of the time series at time 1 and 2 are y1 = eβ0+β1(1) y 1 = e β 0 + β 1 ( 1) and y2 = eβ0+β1(2) y 2 = e β 0 + β 1 ( 2) . The ratio y2 y1 y 2 y 1 is given by:.

is a stationary process, and exhibits weak de-pendence. The other main building block of time series processes is the autoregressive process (AR). The simplest such process, AR(1), is y t= ˆ 1y + et; t= 1;2;::: (2) With the initial condition y0 = 0 and et ˘ (0;˙2 e), yt will be a stable stochastic process if we satisfy the condition jˆ1j< 1.

2021. 12. 7. · Question on weakly stationary. 0. Let Y t is time trend process i.e., Y t = b t + e t for e t follows NID (0, σ 2) Is this process covariance (weakly) stationary? time-series self-study econometrics covariance stationarity. Share.

So I met with my professor and found that z8 is weakly stationary, but I didn't show that to you guys so my apologies. z10 is a non-constant ACF series by the following graphs. The first image represents the first 100 observations and.

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Which among the following is not a necessary condition for constructors? a. Its name must be same as that of class: b. It must not have any return type: c. It must contain a definition body: d. It can contains arguments: Answer: It must contain a definition body.

Solution for Which is not a necessary condition for operating a selected incentive scheme successfully and efficiently? * O The rules of the scheme should be.

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Which of the following conditions are necessary for a series to be classifiable as a weakly stationary process? a. It must have a constant mean b. It must have a constant variance ... It is plausible for financial time series that the optimal value of d could be 2 or 3 d. The estimation of ARIMA models is incompatible with the notion of.

We can classify random processes based on many different criteria. One of the important questions that we can ask about a random process is whether it is a stationary process. Intuitively, a random process $\big\{X(t), t \in J \big\}$ is stationary if its statistical properties do not change by time.

Question: Which of the following conditions are necessary for a time series to be classifiable as a weakly stationary process? (1) It must have a constant mean. (2) It must have a constant variance. (3) It must have constant autocovariances for given time lags. (4) It must have a constant probability distribution.

First, a sufficient and necessary condition for the existence of the weakly stationary solution of the process is presented. The solution is weakly stationary, and the causal expansion of the Markov-switching GARCH process is also established. Second, the general conditions for the existence of any integer-order moment of the square of the.

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5. Which of the following is not a necessary condition for weakly stationary time series? a. Mean is constant and does not depend on time b. Autocovariance function depends on s and t only through their difference |s-t| (where t and s are time scripts) c. The time series under considerations is a finite variance process d. Time series is.

B The condition −1 <φ<1 is necessary for the process to be stationary. To prove this, let us assume that the process begins with z 0 = h, with h being any fixed value. The following value will be z 1 = c+φh+a 1,the next, z 2 = c+φz 1 +a 2 = c+ φ(c+φh+a 1)+a 2 and, substituting successively, we can write: z 1 = c+φh+a 1 z 2 = c(1+φ.

Today · Hjalmarsson (2011) allows for conditional heteroskedasticity but again assumes unconditional homoskedasticity; notice, however, that Hjalmarsson (2011) does not allow for the case where x t is weakly persistent, which as discussed in Remark 12 of Xu (2020), is the case where allowing for conditional heteroskedasticity is most problematic.

11) Which of the following is not a necessary condition for weakly stationary time series? A) Mean is constant and does not depend on time B) Autocovariance function depends on s and t only through their diÙerence |s-t| (where t and s are moments in time) C) The time series under considerations is a Únite variance process D) Time series is Gaussian Solution: (D) A Gaussian time series.

2019. 10. 26. · I know that in order for a stochastic process to be a second-order weakly stationary process. ... once you condition on the amplitude values the series is no longer stationary.) Share. Cite. Improve this answer. ... Browse other questions tagged time-series autocorrelation stationarity or ask your own question.

Statistics and Probability questions and answers Question 3 For an MA (3) process, the following is true p (1) = 1 P (5) = 0 = p (2) = 0 p (3) = 0 and p (5) = 0 Question 4 The following is not a necessary condition for weakly stationary time series?.

a) They are not theoretically motivated b) They cannot produce forecasts easily c) They cannot be used for very high frequency data d) It is difficult to determine the appropriate explanatory variables for use in pure time- series models. 3. Which of the following conditions are necessary for a series to be classifiable as a weakly stationary.

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He feels dizzy and weak. His breathing is shallow. Food poisoning can also result from naturally occurring toxins in some plants and fish. Vomiting and diarrhea can cause dehydration - loss of the fluids required for the normal functioning of the body particularly in babies and small children, so it is.

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Importantly, the m parameter influences the P, D, and Q parameters. For example, an m of 12 for monthly data suggests a yearly seasonal cycle. A P=1 would make use of the first seasonally offset observation in the model, e.g. t-(m*1) or t-12.A P=2, would use the last two seasonally offset observations t-(m * 1), t-(m * 2).. Similarly, a D of 1 would calculate a first order seasonal difference.

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2014. 4. 17. · Please note that in none of these example is the sufficient condition also a necessary condition. For example, it is not necessary to earn 950 points to earn an A in this course. You can earn 920 points to earn an A. (We cannot say that if you do not have 950 points then you can't have an A.).

of weakly dependent time series. Retrospective change detection tests were defined in Gombay (2008) for autoregressive models, and in Berkes et al. (2009) for more.

adaptivity are the necessary conditions for the basis for expanding nonlinear and non-stationary time series; orthogonality is not a necessary criterion for our basis selection for a nonlinear system. The principle of this basis construction is based on the physical time scales that characterize the oscillations of the phenomena. The.

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Which of the following conditions are necessary for a series to be classifiable as a weakly stationary process? (i) It must have a constant mean (ii) It must have a constant variance (iii) It must have constant autocovariances for given lags (iv) It must have a constant probability distribution MCQ Problems / Explanations.

Consider the following model estimated for a time series: yt=yt = 0.3 + 0.5 yt-1 - 0.4 et-1 + et, where et is a zero mean process. ... (iii) are all required for a process to be classifiable as a weakly stationary (or covariance stationary - the two terms are equivalent) process. ... A sufficient but not necessary condition for identification d.

The first difference of a time series is the series of changes from one period to the next. If Y t denotes the value of the time series Y at period t, then the first difference of Y at period t is equal to Y t-Y t-1.In Statgraphics, the first difference of Y is expressed as DIFF(Y), and in RegressIt it is Y_DIFF1. If the first difference of Y is stationary and also completely random (not.

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Two time series models are considered: GARCH processes and generalized multivariate autoregressive equations, Xn +1= An +1 Xn + Bn +1, with nonnegative i.i.d. coefficients. In each case, a necessary and sufficient condition ensuring the existence of a strictly stationary solution is given. Journal of Econometrics 52 (1992) 115-127.

Which of the following conditions are necessary for a series to be classifiable as a weakly stationary process? (i) It must have a constant mean ... These models are particularly useful for time-series forecasting since, even if the RHS variables are exogenous variables, we can produce forecasts from the model without requiring forecasts for.

2022. 7. 28. · AIRLORDS OF HAN by Philip Francis Nowlan is the second half of the seminal Buck Rogers story. It appeared in the March 1929 issues of Hugo Gernsback’s Amazing Stories. As all science fiction fans should recall, Hugo Gernsback is the editor of the first magazine exclusively devoted to science fiction for whom the once-prestigious Hugo Award is.

Stationarity means that the statistical properties of a time series (or rather the process generating it) do not change over time. Stationarity is important because many useful analytical tools and statistical tests and models rely on it. As such, the ability to determine if a time series is stationary is important.

Derive the mean vector and covariance matrix of x t. (b) Derive the necessary and sufficient condition of weak stationarity for x t. Jan 05 2022 12:12 PM. Expert's Answer ... Suppose that z t is a k-dimensional weakly stationary, zero-mean time series following the VARMA(2,q) model where {at} is a white noise series with positive-definite.

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Operant conditioning is a method of learning that occurs through rewards and punishments for behavior. Through operant conditioning, an individual makes an association between a particular behavior and a consequence. B.F Skinner is regarded as the father of operant conditioning and.

A process is called second-order stationary (or weakly stationary) if its mean is constant and its acv.f. depends only on the lag, so that 𝐸[ ( )]=𝜇 And 𝑣[ ( ), ( +𝜏)]= (𝜏) This weaker definition of stationarity will generally be used from now on. Some properties of the autocorrelation function.

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Colons follow independent clauses (clauses that could stand alone as sentences) and Lists/series example: We covered many of the fundamentals in our writing class: grammar, punctuation Phrases that add information or clarify but are not necessary to the meaning of a sentence are ordinarily set.

He feels dizzy and weak. His breathing is shallow. Food poisoning can also result from naturally occurring toxins in some plants and fish. Vomiting and diarrhea can cause dehydration - loss of the fluids required for the normal functioning of the body particularly in babies and small children, so it is.

Which of the following maps can you paint without any adjacent areas being the same color? Which of the following is another name for the soumen noodles traditionally eaten on Tanabata? These cookies are necessary for the website to function and cannot be switched off in our systems. 2016. 11. 22. · We present in this paper a necessary and sufficient condition to establish the inequality between generalized weighted means which share the same sequence of numbers but differ in the weights. We first present a sufficient condition, and then obtain the more general, necessary and sufficient, condition. Our results were motivated by an inequality, involving.

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2015. 7. 17. · Transformation from time domain to frequency ... range of frequency spectrum for discrete time fourier series (DTFS)? a. 0 to 2π b. -π to +π c. Both a & b d. None of the above View Answer / Hide Answer. ANSWER: c. Both a & b . 3. Which among the following assertions represents a necessary condition for the existence of.

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Which of the following monsters would not be affected by global Time debuffs? Which of the following statements about Boss Tonatiuh is wrong? - It has 3 layers of Quantum Shield and will turn into Collapsed state after suffering 3 times of Quantum Explosion.

Operant conditioning is a method of learning that occurs through rewards and punishments for behavior. Through operant conditioning, an individual makes an association between a particular behavior and a consequence. B.F Skinner is regarded as the father of operant conditioning and.

2020. 7. 27. · n PROCEEDINGS OP THE KOYAL SOCIETY OF MED ICINE EDITED BY (October, 1913—May, 1914) JOHN NACHBAR, M.A., M.D. AND (.Tune—July, 1914) J. Y. W. MacALISTER UNDER THE DIRECTION OF.

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The conditions that assure stationarity depend on the nature of the input series and the functions c j(X t). Example To form a nonlinear process, simply let prior values of the input sequence determine the weights. For example, consider Y t= X t+ X t 1X t 2 (2) eBcause the expression for fY tgis not linear in fX tg, the process is nonlinear. Is.

is a stationary process, and exhibits weak de-pendence. The other main building block of time series processes is the autoregressive process (AR). The simplest such process, AR(1), is y t= ˆ 1y + et; t= 1;2;::: (2) With the initial condition y0 = 0 and et ˘ (0;˙2 e), yt will be a stable stochastic process if we satisfy the condition jˆ1j< 1.

2019. 12. 17. · By Exponential rate, we mean growth at a constant rate with continuous compounding. This can be seen as follows: Using the time series formula above, the value of the time series at time 1 and 2 are y1 = eβ0+β1(1) y 1 = e β 0 + β 1 ( 1) and y2 = eβ0+β1(2) y 2 = e β 0 + β 1 ( 2) . The ratio y2 y1 y 2 y 1 is given by:.

The forecast error is -10 +10 -5 +5 +10 1) Which of the following is an example of time series problem? 1. Estimating number of hotel rooms booking in next 6 months. 2. Estimating the total sales in next 3 years of an insurance company. 3. Estimating the number of calls for the next one week. A) Only 3 B) 1 and 2 C) 2 and 3 D) 1 and 3 E) 1,2 and 3.

15. Which of the following is not a necessary condition for weakly stationary time series? (a) * Time series is Gaussian. 3. (b) Mean is constant and does not depend on time. (c) Autocovariance function depends on s and t only through their difference |s- t|(where t and s are moments in time). (d) The time series under considerations is a.

In nature, strictly stationary time series does not exist, and weakly stationary time series is practically considered as stationary time series. In addition to the stationarity, another necessary condition for ergodicity analysis is that the samples from a single realization should be taken from a large enough period of time.

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Which of the following conditions are necessary for a series to be classifiable as a weakly stationary process? (i) It must have a constant mean (ii) It must have a constant variance (iii) It must have constant autocovariances for given lags (iv) It must have a constant probability distribution A:(ii) and (iv) only,B:(i) and (iii) only,C:(i), (ii), and (iii) only,D:(i), (ii), (iii), and (iv).

Which among the following is not a necessary condition for constructors? a. Its name must be same as that of class: b. It must not have any return type: c. It must contain a definition body: d. It can contains arguments: Answer: It must contain a definition body.

The following are my test steps (Note: We are only writing the steps and not all the other parts of the test like the expected result etc.) This is a critical misconception that feeding sample data or input data from the mind memory at the time of executing test cases. If the data is not collected and.

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Solution for Which is not a necessary condition for operating a selected incentive scheme successfully and efficiently? * O The rules of the scheme should be.

Stationarity means that the statistical properties of a time series (or rather the process generating it) do not change over time. Stationarity is important because many useful analytical tools and statistical tests and models rely on it. As such, the ability to determine if a time series is stationary is important.

The proposed method improves the accuracy of the solution without a significant change in the complexity of the system. Since time filters for fluid variables are added as separate post processing steps, the method can be easily incorporated into an existing backward Euler.

We can classify random processes based on many different criteria. One of the important questions that we can ask about a random process is whether it is a stationary process. Intuitively, a random process $\big\{X(t), t \in J \big\}$ is stationary if its statistical properties do not change by time.

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A process is called second-order stationary (or weakly stationary) if its mean is constant and its acv.f. depends only on the lag, so that and No requirements are placed on moments higher than second order. By letting т=0, we note that the form of a stationary acv.f. implies that the variance, as well as the mean, is constant.

Which of the following is not a necessary condition for weakly stationary time from MGT ORGANIZATI at Eastern Gateway Community College.

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Stationarity means that the statistical properties of a time series (or rather the process generating it) do not change over time. Stationarity is important because many useful analytical tools and statistical tests and models rely on it. As such, the ability to determine if a time series is stationary is important.

Which of the following conditions are necessary for a series to be classifiable as a weakly stationary process? (i) It must have a constant mean (ii) It must have a constant variance (iii) It must have constant autocovariances for given lags (iv) It must have a constant probability distribution MCQ Problems / Explanations.

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stationary solution and conditions under which such a solution is unique. The purposes of this note are to establish necessary and su-cient conditions on both the i.i.d. noise and the zeroes of the deflning polynomials in (1.1) under which a strictly stationary solution (Yt)t2Zof the equations (1.1) exists, to specify a solution when these.

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If the time series is not stationary, we can often transform it to stationarity with one of the following techniques. We can difference the data. That is, given the series \(Z_t\), we create the new series $$ Y_i = Z_i - Z_{i-1} \, . $$ The differenced data will contain one less point than the original data. Although you can difference the data.

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the moving average method is one of the most complex smoothing techniques used for processing time series. false. the exponential smoothing method weighs all available observations in a time series equally. false. the exponential trend model is attractive when the increase in the series gets larger over time. true. A process is called second-order stationary (or weakly stationary) if its mean is constant and its acv.f. depends only on the lag, so that and No requirements are placed on moments higher than second order. By letting т=0, we note that the form of a stationary acv.f. implies that the variance, as well as the mean, is constant.

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Colons follow independent clauses (clauses that could stand alone as sentences) and Lists/series example: We covered many of the fundamentals in our writing class: grammar, punctuation Phrases that add information or clarify but are not necessary to the meaning of a sentence are ordinarily set.

6 Stationarity is a desirable property for a time series process. A TRUE. B FALSE. View Answer. 7 Imagine, you are working on a time series dataset. Your manager has asked you to build a highly accurate model. You started to build two types of models which are given below. Model 1: Decision Tree model. Model 2: Time series regression model.

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C is correct. (i) to (iii) are all required for a process to be classifiable as a weakly stationary (or covariance stationary - the two terms are equivalent) process. The final condition of having a constant probability distribution is a stronger condition than the first three, since it applies to the whole distribution whereas the first three conditions only apply to the first two moments of.

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Transcribed image text: Which of the following is not a necessary condition for inference about a mean using a z test? O We know the value of o. O We have a simple random sample. The population of the variable that we are measuring has a Normal distribution.

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. Questions 35 through 38 are based on the following reading. The First Amendment to the American Constitution declares freedom Further scientific study indicates that these represent a type of time line of events - past, present, and future. Many of the events have been interpreted. Time Series and Statistics Necessary A time series is a realization of a sequence of random variables. CDF P(X x) = F X(x) ... their joint distribution does not change in the following sense. Strictly stationary time series [Def 1.6 in the book] I For F t 1;t 2 ... Weakly Stationary time series [Def 1.7 in the book] X t is weakly stationary if. 2015. 7. 17. · Transformation from time domain to frequency ... range of frequency spectrum for discrete time fourier series (DTFS)? a. 0 to 2π b. -π to +π c. Both a & b d. None of the above View Answer / Hide Answer. ANSWER: c. Both a & b . 3. Which among the following assertions represents a necessary condition for the existence of. Derive the mean vector and covariance matrix of x t. (b) Derive the necessary and sufficient condition of weak stationarity for x t. Jan 05 2022 12:12 PM. Expert's Answer ... Suppose that z t is a k-dimensional weakly stationary, zero-mean time series following the VARMA(2,q) model where {at} is a white noise series with positive-definite.

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b. Watch the following video and make a mind map of the information that is presented on the video. CASE STUDY: ACQUIRING METROT Action minutes MINUTE OF THE SENIOR MANAGERS Date: 29 March Present: Diana Marcela Tinjacá, John González and Josh Marin. Which of the following is a way of starting a formal letter? (A). Thank you for your letter dated 26th August 2005. (B). Thanks for your letter, it was Give Jane my best wishes. 5. Which of the following is NOT a suitable final sentence for a formal letter? (A). I look forward to hearing from you soon. Not the worst pairing he could’ve had, I suppose? “Anyways. I talked to Lucy, you know, my fiancé, on the ride here. She wants me to come home, but I’ve gotten used to having you around.” Marcel took a deep breath, scratching his stubbly scalp. “Ah, maybe it’s not the right time to ask, after what I just told you.” “No, I’m. Curious Episode in History. Historic Emblem. 1. Almost everybody has heard of the ancient Maya, a mysterious people who lived in Central America in 1500 ВС — AD 900 and then suddenly disappeared. , then it is easily seen that the conditions above become the classical conditions defining a weakly stationary process. Gray and Zhang (1988) show that the time series Yuu ∈ − , defined by Yu =Xt where t=eu is stationary if and only if Xt is M-stationary. The process Yu is referred to as the dual of Xt . Thus,.

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A process is called second-order stationary (or weakly stationary) if its mean is constant and its acv.f. depends only on the lag, so that and No requirements are placed on moments higher than second order. By letting т=0, we note that the form of a stationary acv.f. implies that the variance, as well as the mean, is constant.

A time series { X t}with E(2 t) <∞is called weakly stationary or just stationary if E(X t1) = E(X t2) and cov(X t1;X t2) = cov(X t1+˝;X t2+˝) for all t 1; 2 and ˝. If {X t}is a weakly stationary TS then obviously the expectation of X t does not depend on t, i.e. X t = for some and for all times t, the ACVF (t+ ˝; )=0) ˝ may be viewed as.

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a) They are not theoretically motivated b) They cannot produce forecasts easily c) They cannot be used for very high frequency data d) It is difficult to determine the appropriate explanatory variables for use in pure time- series models. 3. Which of the following conditions are necessary for a series to be classifiable as a weakly stationary.

A process is called second-order stationary (or weakly stationary) if its mean is constant and its acv.f. depends only on the lag, so that 𝐸[ ( )]=𝜇 And 𝑣[ ( ), ( +𝜏)]= (𝜏) This weaker definition of stationarity will generally be used from now on. Some properties of the autocorrelation function.

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28) Excursion time. 35) Size of the/a group.

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Necessary conditions are selected from these relations (the maximum number The obtained regular expressions lead us to a sufficient condition for the Fred-holm property of the given Stationary Problem of Complex Heat Transfer in a System of Semitransparent Bodies with Boundary Conditions.

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C is correct. (i) to (iii) are all required for a process to be classifiable as a weakly stationary (or covariance stationary - the two terms are equivalent) process. The final condition of having a constant probability distribution is a stronger condition than the first three, since it applies to the whole distribution whereas the first three conditions only apply to the first two moments of.

8.1 Stationarity and differencing. A stationary time series is one whose properties do not depend on the time at which the series is observed. 14 Thus, time series with trends, or with seasonality, are not stationary — the trend and seasonality will affect the value of the time series at different times. On the other hand, a white noise series is stationary — it does not matter when you.

2021. 6. 24. · There are 4 necessary conditions for Deadlock to occur:1) Mutual Exclusion2) No pre-emption3) Hold and Wait4) Circular waitOption (B) is correct. Which of the following is not a necessary condition for deadlock?a)Mutual exclusionb)Reentrancyc)Hold and waitd)No pre-emptionCorrect answer is option 'B'.

The aim of this article is to give a simpler, more usable sufficient and necessary condition to the regularity of generic weakly stationary time series. Also, this condition is used to show how a regular process can be approximated by a lower rank regular process. The relevance of these issues is shown by the ever increasing presence of high.

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28) Excursion time. 35) Size of the/a group.

In mathematics and statistics, a stationary process (or a strict/strictly stationary process or strong/strongly stationary process) is a stochastic process whose unconditional joint probability distribution does not change when shifted in time. Consequently, parameters such as mean and variance also do not change over time. To get an intuition of stationarity, one can imagine a frictionless.

C is correct. (i) to (iii) are all required for a process to be classifiable as a weakly stationary (or covariance stationary - the two terms are equivalent) process. The final condition of having a constant probability distribution is a stronger condition than the first three, since it applies to the whole distribution whereas the first three conditions only apply to the first two moments of.

Which of the following conditions are necessary for a series to be classifiable as a weakly stationary process? (i) It must have a constant mean (ii) It must have a constant variance (iii) It must have constant autocovariances for given lags (iv) It must have a constant probability distribution A:(ii) and (iv) only,B:(i) and (iii) only,C:(i), (ii), and (iii) only,D:(i), (ii), (iii), and (iv).

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Answer (1 of 8): A statement P is called a necessary condition for statement Q if P is true whenever Q is true . P is a sufficient condition for Q if Q is true whenever P is true . P is said to be a necessary and sufficient condition for Q if P and Q are both true (or both false) together . Her.

A) Mean is constant and does not depend on time. B) Autocovariance function depends on s and t only through their difference |s-t| (where t and s are moments in time) C) The time series under considerations is a finite variance process. D) Time series is Gaussian.

2016. 2. 10. · is a stationary process, and exhibits weak de-pendence. The other main building block of time series processes is the autoregressive process (AR). The simplest such process, AR(1), is y t= ˆ 1y + et; t= 1;2;::: (2) With the initial condition y0 = 0 and et ˘ (0;˙2 e), yt will be a stable stochastic process if we satisfy the condition jˆ1j< 1. If time series data are non stationary then the regression results based on the ordinary least squares [OLS] method will be spurious. In other words the determination of order of integration of each time series variable is required. This objective will be attained by unit root testing of the time series.

stationary solution and conditions under which such a solution is unique. The purposes of this note are to establish necessary and su-cient conditions on both the i.i.d. noise and the zeroes of the deflning polynomials in (1.1) under which a strictly stationary solution (Yt)t2Zof the equations (1.1) exists, to specify a solution when these. Transcribed image text: Which of the following is not a necessary condition for inference about a mean using a z test? O We know the value of o. O We have a simple random sample. The population of the variable that we are measuring has a Normal distribution.

This is an AR(1) model only if there is a stationary solution to φ(B)X t = W t , which is equivalent to |φ 1 | 6= 1. This is equivalent to the following condition on φ(z) = 1− φ 1 z:.

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is a stationary process, and exhibits weak de-pendence. The other main building block of time series processes is the autoregressive process (AR). The simplest such process, AR(1), is y t= ˆ 1y + et; t= 1;2;::: (2) With the initial condition y0 = 0 and et ˘ (0;˙2 e), yt will be a stable stochastic process if we satisfy the condition jˆ1j< 1.

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