R-studio 5

| Posted on by

A & R Recording Inc. was a major American independent studio recording company founded in 1958 by Jack Arnold[a][1] and Phil Ramone.[2][3]

History[edit]

Before founding A & R Recording in 1958, Arnold and Ramone had been working at JAC Recording, Inc.; Arnold had been a partner at JAC. The 'A' and 'R' initials were derived from their surnames. But also, Arnold and Ramone relished the idea that their initials and company name matched the industry acronym for 'artist and repertoire,' an important avocation in the recording industry.[4]

Mar 11, 2019 R-3.5.3 for Windows (32/64 bit) Download R 3.5.3 for Windows (79 megabytes, 32/64 bit) Installation and other instructions. New features in this version. If you want to double-check that the package you have downloaded matches the package distributed by CRAN, you can compare the md5sum of the.exe to the fingerprint on the master server. 5.1.1 Benefits of Using R. Reproducibility: Standardized processes (e.g., functions, loops, documentation) When using MS Excel processes are often spread across multiple sheets or calculations are performed haphazardly within a single sheet. In general, this makes it very hard to interpret processes preformed and to reproduce the process.

Jack Arnold ended his association with A & R Recording shortly after co-founding it, due to health issues.

  1. Inventory Records (1) View inventory records anonymously contributed by opt-in users of the K1000 Systems Management Appliance. Uninstall String. C: Program Files (x86) R-Studio Uninstall.exe C: Program Files R-Studio Uninstall.exe.
  2. R-Studio 8.5 Build 170117 Network Edition Multilingual. Showing 2 download results of 2 for R Studio 5.1. R Studio 5.1 Download Search Tips. To create more accurate search results for R Studio 5.1 try to exclude using commonly used keywords such as: crack, download, serial, keygen.
  3. For persistent errors of type, first, ensure you are working with the latest version of R. The installr package is a very convenient way to do this. Then, start new R session (ideally, not in RStudio). Uninstall tidyverse, tidyselect, and rlang. # if you are using multiple libraries, you may need to specify libpath, # using the following.

Original A & R studio — 112 West 48th Street[edit]

The original studio was in Midtown Manhattan, New York City, on the 4th floor of Mogull's Film & TV[b] building at 112 West 48th Street. The studio was named 'Studio A1.' Manny's[c][5] — a famous music instrument retailer — was one-half of the first 3 floors; Mogull's Film & TV was the other half. Jim and Andy's Bar,[d][6] an important hangout for studio musicians was next door at 116 West 48th Street. Ramone installed an intercom from the studio to Jim & Andy's to call for musicians if someone didn't show-up.[7][4]

In the first studio, Ramone quickly gained a reputation as a good sound engineer and music producer, in particular for his use of innovative technology. According to David Simons, author, the original studio at 112 West 48th St., which was started on a shoestring budget, remains Ramone's greatest legacy.[4]

The studio was designed for the purpose of doing demos. According to Ramone, the room, 11.5 metres (38 ft) by 12 metres (39 ft), had an incredibly unique sound. He attributed much of it to the height of 3.6 metres (12 ft) and before long clients were requesting to do their final tapes there and in no uncertain terms letting it be known that this was nomere demo studio. In a short period of time, Ramone felt the need to upgrade the equipment.

Second studio, Studios A-1 and A-2 — 799 7th Avenue[edit]

In October 1967, A & R purchased Columbia'sStudio A on the 7th floor at 799 7th Avenue at 52nd Street[8][9] and leased the space, which consisted of about 10,000 square feet (929.0304 m2)[10]Columbia had owned the studio since the 1930s.

Capacities, as published in 1974:[11]
Studio A-1: 40 x 50 feet; height 30 feet – 1,600 square feet (148.6449 m2) – accommodated 90 people
Studio A-2: 25 x 30 feet; height 12 feet – 750 square feet (69.6773 m2) – accommodated 20 people

Third studio, Studios R-1 and R-2 — 322 West 48th Street[edit]

A & R added a third studio in the Leeds Music Corporation building at 322 West 48th Street. A & R became part owner of the building, a 6-story building, and designed recording studios on the first and second floors, named R1 and R2, respectively. The 'R' stood for 'Ramone.' A & R also occupied the basement.[4] 322 West 48th Street is currently the home of American Federation of Musicians Local 802, the New York City musicians' union and the Jazz Foundation of America.

Capacities, as published in 1974:[11]
Studio R-1: 38 x 28 feet; height 13-3/4 feet – 1,064 square feet (98.8488 m2) – accommodated 26 people
Studio R-2: 20 x 25 feet; height 13 feet – 500 square feet (46.4515 m2) – accommodated 12 people

Launch of A & R Records[edit]

In February 1970, A & R Recording launched A & R Records,[12][13] a company that produced albums of artists that included Paul Simon, Billy Joel, George Barnes (musician) and Bucky Pizzarelli.

Satellite studios[edit]

In 1970, A & R Recording formalized two partnerships to build two satellite studios, one with Brooks Arthur (né Arnold Brodsky; born 1936)[e] in Blauvelt, New York, and one with Norman (Norm) Fuller Vincent (1930–2014) in Jacksonville, Florida.

914 Sound Studios[edit]

The partnership with Arthur was named '914 SRS' and was located at 34 NY Route 303 in Blauvelt. 'SRS stood for 'Sound Recording Studios.' The legal structure of the partnership was in the form of a New York corporation operating as a wholly owned subsidiary of A & R Recording Inc. The entity name was '914 Sound Recording Studios, Inc.' The studio, a converted gas station, opened October 1970. Arthur owned one-half, Ramone, Don Frey,[f] and Arthur Downs Ward (1922–2002) owned the other half.[14][15] They sold it in 1978 and the corporation — 914 Sound Recording Studios, Inc. — dissolved in 1982.

Vincent SRS[edit]

The partnership with Norman Vincent, et al. was named 'Vincent SRS' and was located in Jacksonville, Florida, and opened November 1970. Vincent was the operator.

Closing[edit]

A & R Recording closed in 1989.

Selected artists[edit]

Artists produced by Ramone include

Neighborhood[edit]

In a 10-block area of midtown Manhattan during the disco era, there was Media Recording, Hit Factory, Sony, and A&R Recording had two buildings. And last but certainly not least, Record Plant Recording studios @ 321 W. 44th Street, with four studios, duplication room, two mobile recording trucks, and the master cutting room, and the Record Plant Shop.

  1. A & R Recording Inc.
    112 West 48th Street
    Opened by Jack Arnold and Phil Ramone 1959. Corner of 6th Avenue, next door to Jim & Andy's Bar (116 West 48th Street) and Manny's Music (156 West 48th Street), both famous musicians hangouts. Used regularly by Tom Dowd for Atlantic sessions and producer Creed Taylor for Verve. Van Morrison recorded 'Brown Eyed Girl' there.
  2. A & R Studio 2 (formerly Columbia Studio A)
    799 7th Avenue
    Opened by Jack Arnold and Phil Ramone early 1968
  3. Associated Sound (now Quad Recording Studios)
    723 7th Avenue
    Near corner of West 48th Street, a few doors down from Dick Charles. The Angels' 'My Boyfriend's Back,' the Raindrops'
    'What A Guy' and The McCoys' 'Hang On Sloopy' were cut there
  4. Bell Sound (later The Hit Factory)
    237 West 54th Street
    Founded June 1950 by Allen Weintraub and Daniel Cronin (1929–1968), both classmates from Brooklyn Technical High School; studio was located at 135 West 54 beginning June 1959; Burt Bacharach's favorite studio. Bought by Jerry Ragovoy 1968 and reopened as The Hit Factory; sold 1975 to partner Eddie Germano (né Edward F. Germano; 1941–2003); now run by Troy George Germano (born 1962), his son
  5. Capitol Studios, Studio A (Capitol Records, Inc.)
    (the studio operated under Capitol from 1949 to 1961)
    151 West 46th Street
    First floor (one floor up) in the 14-story Eaves Building (built in 1928). The Eaves Costume Company – founded by Albert Grammer Eaves (1847–1900) in 1863 (158 years ago), and still in existence – occupied the ground floor.
  6. Century Sound
    135 West 52nd Street
    One flight up. Former radio studio. Opened by Brooks Arthur in 1967
  7. Columbia 30th Street
    207 East 30th Street
    Converted Armenian church. Opened 1949, closed mid-1982, torn-down, now an apartment building
  8. Columbia Studio A (later A & R Studio R2)
    799 7th Avenue
    Opened in the 1930s. Columbia's main facility prior to East 30th Street. Sold to A & R late 1967
  9. Columbia Studio B
    49 East 52nd Street
    Former site of CBS Radio Network building, near Madison Avenue. Opened late 1967
  10. Dick Charles
    729 7th Avenue
    Small demo studio, near corner of West 48th Street, a few doors up from Associated. Many of S'pop's favored songwriters recorded demos there
  11. Mira Sound
    145-155 West 47th Street
    On the ground floor of the Hotel America, now a Euro-style hotel. Recorded there: 'Remember (Walking in the Sand)' by The Shangri-Las and 'Society's Child' by Janis Ian
  12. The Power Station (now Avatar Studios)
    441 West 53rd Street
    Near 10th Avenue. Founded 1977 by Tony Bongiovi. Previously home to ConEdison (hence Power Station)
  13. RCA
    155 East 24th Street
    Near Lexington Avenue
  14. RCA Webster Hall
    125 11th Street
    In the East Village. Built late 1800s. Converted by RCA early 1950s. Now a nightclub
  15. The Record Plant (later Streetlight)
    321 West 44th Street
    Once home to Warner Brothers Pictures; opened by Gary Kellgren and Chris Stone in 1968
  16. Stea-Philips
    7th Avenue
    Corner 51st Street, close to Columbia Studio A and 1650 Broadway. Owner: Lenny Stea (né Leonard J. Stea; born 1928). The Four Seasons cut 'Sherry' there
  17. Talentmasters Recording Studio
    126 West 42nd Street
    Owners: Bob Gallo and Robert (Bob) Harvey. Later bought out by Atlantic
    The Who recorded there
  18. World United
    1595 Broadway
    Owner: Harry Lookofsky, aka Hash Brown, father of Michael Brown of The Left Banke, who recorded 'Walk Away Renée' there
  19. JAC Recording, Inc.
    152 West 58th Street
    Owner: Charles Leighton
    This is where Phil Ramone got his start
  20. Allegro Sound Studios
    1650 Broadway
    Owner (original): Kama Sutra Records This was actually on the 51st Street side of the 1650 Broadway building, located in the basement, around the corner from the famous jazz club Birdland. Originally a demo studio for Kama Sutra, it was then purchased by Laurie Records, who gave it an extensive upgrade under chief engineer Bruce Staple. After several changes in ownership, it became known as Generation Sound Studios in the 1970s. Many of the Tommy James hits were recorded there, including I Think We're Alone Now and Crimson And Clover. After the departure of Bruce Staple, Tony May of A&R became chief engineer.

Personnel[edit]

In 1972, management of A & R included Robert Gerics (general manager & studio manager), Nick Diminno (studio manager), and Irving Joel (chief engineer). The studio was located at 322 West 48th Street.[16]

Management and shareholders

A & R Recording Inc.

  • Art Ward, president of the parent company
  • Phil Ramone, vice president & creative director
  • John Gordy, president of Visual Sounds, Inc. (VSI), A & R's video subsidiary
  • Don Frey (né Donald Gregory Frey; born 1927) had been a senior sound mixer at NBC TV in the late 1950s. He became vice president of operations at A & R Recording and ended-up being a partner at A & R for 25 years. He personally engineered sessions for Ray Charles, Nina Simone, Ike and Tina Turner, and many others. During the 1960s, Frey engineered some of the biggest commercials of the decade at A & R, including one of the Yankees theme and ads for Marlboro and Pepsi. Frey's recording sessions involved 40 and 50 people in the room. Frey, in 1988, was instrumental in rebuilding BMG's Studio A in New York.
According to a 1978 trade magazine article by studio engineer Malcolm Addey, Frey, while a mixer at NBC TV, had been moonlighting at A & R and did a lot of the installation work. His work there became more than he could handle on a part-time basis and he accepted an invitation to work full-time. Don was eventually invited to invest and became vice president in charge of operations.[3][4]
  • Brooks Arthur Productions, Inc., founded in 1999 as a California corporation, is active and based in Encino, California, and is headed by Arthur.

A & R Records (subsidiary)

  • Ed Barsky (né Edward Sydney Barsky; 1924–1993), president of A & R Records, based in Los Angeles (founded 1970)
  • Irving 'Bud' Dain, vice president of A&R and promotion
  • Harriet Margulies, public relations (worked from New York)

Engineers

  • Brooks Arthur, engineer
  • Roy Cicala, engineer
  • David Greene, engineer, producer
  • Roy Halley, engineer
  • Irving Joel, chief engineer
  • Bob Ludwig, mastering engineer
  • Tony May, engineer
  • Elliot Scheiner, engineer, worked 7 years at A & R
  • Bill Schwartau (né William H. Schwartau; 1926–1985) appointed Chief Engineer at A & R Recording, December 1958[17]
  • Norman Schwartz (1928–1995), studio technician & sound consultant
  • David Smith, chief engineer
  • Fred Weinberg, engineer, producer
  • Shelly Yakus, engineer

Studio managers

  • Nick Diminno, studio manager
  • Robert Gerics, general manager & studio manager
  • Mitch Plotkin, studio manager

Notes[edit]

  1. ^Jack Arnold was also known as Jack Aaron. (A Different Drummer: What Makes Me Tic, a Memoir, by Herbert Wasserman, 1922–2001, Writers Club Press, 2000, pg. 134; OCLC52229234)
  2. ^Mogull Bros. Electrical Corp., incorporated in New York in 1923, sold radios. The incorporators were Charles (1898–1986), Leo (1894–1962), and Peter Mogull (1892–1964). Out of that, the brothers founded the Film Library, a pro and retail film sales and rentals, cinema equipment, and camera firm, first at 68 W 48th Street, then, as of 1951, at 122 W 48th Street. When A & R Recording leased its first studio at 122 W 48th, the only surviving brother, Charles, was the landlord. One of Charlie's son's, Artie Mogull (1927–2004), had been an executive for M. Witmark & Sons and a notable A&R executive producer of many rising stars in jazz and rock, among whom included Bob Dylan. In 1950, Mogull's Camera & Film Exchange Inc. sold the building at 112-114 West 48th St. to Kenchal Estates Inc. ('Manhattan Transfers,' The New York Times, September 23, 1950)In 1944, the building at 112-114 W 48th St. was sold by The City Bank Farmers Trust Company to 112 West 48th Street, Inc., Frederick Dreier, president. ('$77,500 Consideration,'New York Sun, July 10, 1944, pg. 22, col. 7)
    Past tenants at 112-114 W 48th St. include:
    1. Winitzki Chess Club (1942), Eugenie Club (1925)
    2. In 1929, it was the Green Room Grill, one of the largest speakeasies in the Theatre District. The Friar's Club, at 106-108-110 W 48th Street, was next door
    3. In 1942, the building housed the Musical Instrument Exchange, Inc., operated by Samuel Goodman, aka Kelly Goodman
    4. Soloman Pfeiffer (1881–1936), seller of imported violins (from the late 1890s to about 1925)
  3. ^Manny Goldrich (né Manuel Kaufman Goldrich; 1904–1968), originally a saxophone salesman, founded Manny's Musical Instruments & Accessories Inc. in 1933 on West 48th Street. In 1940 though 1959, the address was 120 W 48th St. The store endured under three generations of Goldriches. In 1999, The Goldrich heirs sold the store and the brownstone building at 156 West 48th Street to its chainstore rival across the street, Sam Ash Music, who, in turn, maintained Manny's as a subsidiary and retained its staff and family managers until 2009. Manny's had, until about 1969, been located at 112 West 48th Street.
  4. ^Jim & Andy's bar was founded in 1945, presumably by partner's named Jim and Andy. Jim Koulouvaris (né James Daniel Koulouvaris; 1917–1972) bought it in 1955. From 1945 to about 1968, it had been located at 116 West 48th St. Notable employees included Pete Salvato (1908–1969), chief cook for 17 years. Rocky Mareno was Jim's bartender. (see Meet Me At Jim & Andy's in the citations below)
  5. ^Brooks Arthur — as a songwriter in 1959 — used the pseudonyms Arnie Blaine and Art Barrett. From 1960 on (the last sixty-one years), he has been known as Brooks Arthur.
  6. ^Don Frey, a former senior sound mixer at NBC, was vice president of operations at A & R Recording. Frey, in 1988, was instrumental in rebuilding BMG's Studio A in New York.

R-studio 5.0

References[edit]

  1. ^A Different Drummer: What Makes Me Tic, a Memoir, by Herbert Wasserman (1922–2001), Writers Club Press (2000), pg. 134; OCLC52229234
  2. ^Temples of Sound: Inside the Great Recording Studios, by Jim Cogan & William Clark, San Francisco: Chronicle Books (2003); OCLC49553469
  3. ^ ab'A & R Recording, New York,' by Malcolm Thomas Addey (born 1933), Studio Sound and Broadcast Engineering, December 1978; ISSN0144-5944
    Note: Addey is a prolific recording studio audio engineer known for is work with The Beatles at Abbey Road Studios
  4. ^ abcdeHow the Great New York Records Were Made, Dave Simons, Backbeat Books (2004); OCLC57543979
  5. ^'Jim and Andy's: A Musician's Bar,' by Steven A. Cerra, September 4, 2014
  6. ^Playing The Changes: Milt Hinton's life in stories and photographs, by Milt Hinton, Vanderbilt University Press (2008); OCLC156975394
  7. ^Meet Me At Jim & Andy's: Jazz Musicians and Their World, by Gene Lees, Oxford University Press (1988); OCLC17677072
  8. ^Making records: the Scenes Behind the Music,Phil Ramone & Charles L. Granata, New York: Hyperion Books (2007), pps. 136–137; OCLC174143979
  9. ^How Does It Sound Now? by Gary Gottlieb, Course Technology (2010), pg. 57; OCLC535576372 (pdf copy)
  10. ^'Studio Space Leased,' The New York Times, October 16, 1967
  11. ^ ab'A Guide to New York City Studios,'Billboard, December 14, 1974, pg. 46
  12. ^'1972 A&R Studios Setting Up Small Satellites', by Radcliffe Joe (died 2004), Billboard, September 19, 1970, pps. 3 & 8
  13. ^'Fla. Studio Opening Marks A&R 'Bring Facility to Artists' Move', Billboard, October 24, 1974, pg. 10
  14. ^'Classic Tracks: Janis Ian's 'At Seventeen,' by Gary Eskow, Mix, June 1, 2005 (retrieved March 30, 2013)
  15. ^'Legendary Producer Phil Ramone Dies at Age 79,' by Mike Barnes, Billboard, March 30, 2013 (retrieved March 31, 2013)
  16. ^'1972 International Directory of Recording Studios', Billboard, June 10, 1972, pg. RS 38
  17. ^Paid Announcement: 'A & R Recording Incorporated,'Billboard, December 15, 1958, pg. 81
Retrieved from 'https://en.wikipedia.org/w/index.php?title=A_%26_R_Recording&oldid=1037313787'
5.0

Since the seminal paper of Sims (1980) vector autoregressive models have become a key instrument in macroeconomic research. This post presents the basic concept of VAR analysis and guides through the estimation procedure of a simple model. When I started my undergraduate program in economics I occasionally encountered the abbreviation VAR in some macro papers. I was fascinated by those waves in the boxes titled impulse responses and wondered how difficult it would be to do such reseach on my own. I was motivated, but my first attempts were admittedly embarrassing. It took me quite a long time to figure out which kind of data can be analysed, how to estimate a VAR model and how to obtain meaningful impulse responses. Today, I think that there is nothing fancy about VAR models at all once you keep in mind some points.

Univariate autoregression

VAR stands for vector autoregression. To understand what this means, let us first look at a simple univariate (i.e. only one dependent or endogenous variable) autoregressive (AR) model of the form (y_{t} = a_1 y_{t-1} + e_t). In this model the current value of variable (y) depends on its own first lag, where (a_1) denotes its parameter coefficient and the subscript refers to its lag. Since the model contains only one lagged value the model is called autoregressive of order one, short AR(1), but you can easily increase the order to p by adding more lags, which results in an AR(p). The error term (e_t) is assumed to be normally distributed with mean zero and variance (sigma^2).

Stationarity

Before you estimate such a model you should always check if the time series you analyse are stationary, i.e. their means and variances are constant over time and do not show any trending behaviour. This is a very important issue and every good textbook on time series analysis treats it quite – maybe too – intensively. A central problem when you estimate models with non-stationary data is, that you will get improper test statistics, which might lead you to choose the wrong model.

There is a series of statistical tests like the Dickey-Fuller, KPSS, or the Phillips-Perron test to check whether a series is stationary. Another very common practise is to plot a series and check if it moves around a constant mean value, i.e. a horizontal line. If this is the case, it is likely to be stationary. Both statistical and visual tests have their drawbacks and you should always be careful with those approaches, but they are an important part of every time series analysis. Additionally, you might want to check what the economic literature has to say about the stationarity of particular time series like, e.g., GDP, interest rates or inflation. This approach is particularly useful if you want to determine whether a series trend or difference stationary, which must be treated a bit differently.

At this point it should be mentioned that even if two time series are not stationary, a special combination of them can still be stationary. This phenomenon is called cointegration and so-called (vector) error correction models (VECM) can be used to analyse it. For example, this approach can significantly improve the results of an analysis of variables with known equilibrium relationships.

Autoregressive distributed lag models

Regressing a macroeconomic variable solely on its own lags like in an AR(p) model might be a quite restrictive approach. Usually, it is more appropriate to assume that there are further factors that drive a process. This idea is captured by models which contain lagged values of the dependent variable as well as contemporaneous and lagged values of other, i.e. exogenous, variables. Again, these exogenous variables should be stationary. For an endogenous variable (y_{t}) and an exogenous variable (x_{t}) such an autoregressive distributed lag, or ADL, model can be written as

[y_{t} = a_1 y_{t-1} + b_0 x_{t}+ b_{1} x_{t-1} + e_t.]

In this ADL(1,1) model (a_1) and (e_t) are definded as above and (b_0) and (b_1) are the coefficients of the contemporaneous and lagged value of the exogenous variable, respectively.

The forecasting performance of such an ADL model is likely to be better than for a simple AR model. However, what if the exogenous variable depends on lagged values of the endogenous variable too? This would mean that (x_{t}) is endogenous too and there is further space to improve our forecasts.

Vector autoregressive models

5 Number Summary Rstudio

At this point the VAR approach comes in. A simple VAR model can be written as

[begin{pmatrix} y_{1t} y_{2t} end{pmatrix} = begin{bmatrix} a_{11} & a_{12} a_{21} & a_{22} end{bmatrix} begin{pmatrix} y_{1t-1} y_{2t-1} end{pmatrix} + begin{pmatrix} epsilon_{1t} epsilon_{2t} end{pmatrix}]

or, more compactly,

[ y_t = A_1 y_{t-1} + epsilon_t,]where (y_t = begin{pmatrix} y_{1t} y_{2t} end{pmatrix}), (A_1= begin{bmatrix} a_{11} & a_{12} a_{21} & a_{22} end{bmatrix}) and (epsilon_t = begin{pmatrix} epsilon_{1t} epsilon_{2t} end{pmatrix}.)

Note: Yes, you should familiarise yourself with some (basic) matrix algebra (addition, subtraction, multiplication, transposition, inversion and the determinant), if you want to work with VARs.

Basically, such a model implies that everything depends on everything. But as can be seen from this formulation, each row can be written as a separate equation, so that (y_{1t} = a_{11} y_{1t-1} + a_{12} y_{2t-1} + epsilon_{1t}) and (y_{2t} = a_{21} y_{1t-1} + a_{22} y_{2t-1} + epsilon_{2t}). Hence, the VAR model can be rewritten as a series of individual ADL models as described above. In fact, it is possible to estimate VAR models by estimating each equation separately.

Looking a bit closer at the single equations you will notice, that there appear no contemporaneous values on the right-hand side (rhs) of the VAR model. However, information about contemporaneous relations can be found in the so-called variance-covariance matrix(Sigma). It contains the variances of the endogenous variable on its diagonal elements and covariances of the errors on the off-diagonal elements. The covariances contain information about contemporaneous effects between the variables. Like the error variance (sigma^2) in a single equation model (Sigma) is essential for the calculation of test statistics and confidence intervals.

The covariance matrices of standard VAR models are symmetric, i.e. the elements to the top-right of the diagonal (the “upper triangular”) mirror the elements to the bottom-left of the diagonal (the “lower triangular”). This reflects the idea that the relations between the endogenous variables only reflect correlations and do not allow to make statements about causal relationships, since the effects are the same in each direction. This is the reason why this model is said to be not uniquely identified.

Contemporaneous causality or, more precisely, the structural relationships between the variables is analysed in the context of so-called structural VAR (SVAR) models, which impose special restrictions on the covariance matrix – and depending on the model on other matrices as well – so that the system is identified. This means that there is only one unique solution for the model and it is clear, how the causalities work. The drawback of this approach is that it depends on the more or less subjective assumptions made by the researcher.1 For many researchers this is too much subjectiv information, even if sound economic theory is used to justify those assumptions.

In this article I consider a VAR(2) process of the form

[begin{pmatrix} y_{1,t} y_{2,t} end{pmatrix} =begin{bmatrix} -0.3 & -0.4 0.6 & 0.5 end{bmatrix} begin{pmatrix} y_{1,t-1} y_{2,t-1} end{pmatrix} +begin{bmatrix} -0.1 & 0.1 -0.2 & 0.05 end{bmatrix} begin{pmatrix} y_{1,t-2} y_{2,t-2} end{pmatrix} +begin{pmatrix} epsilon_{1t} epsilon_{2t} end{pmatrix}]

with (epsilon_{1t} sim N(0, 0.5)) and (epsilon_{2t} sim N(0, 0.5)). Note that for simplification the errors are not correlated. Models with correlated errors are described in a post on SVAR.

The artificial sample for this example is generated in R with

Estimation

The estimation of the parameters and the covariance matrix of a simple VAR model is straightforward. For (Y = (y_{1},..., y_{T})) and (Z = (z_{1},..., z_{T})) with (z) as a vector of lagged valus of (y) and possible deterministic terms the least squares estimator of the parameters is (hat{A} = YZ(ZZ')^{-1}). The covariance matrix is then obtained from (frac{1}{T-Q}(Y-hat{A}Z) (Y-hat{A}Z)'), where (Q) is the number of estimated parameters. These formalas are usually already programmed in standard statistics packages for basic applications.

In order to estimate the VAR model I use the vars package by Pfaff (2008). The relevant function is VAR and its use is straightforward. You just have to load the package and specify the data (y), order (p) and the type of the model. The option type determines whether to include an intercept term, a trend or both in the model. Since the artificial sample does not contain any deterministic term, we neglect it in the estimation by setting type = 'none'.

Model comparison

A central issue in VAR analysis is to find the number of lags, which yields the best results. Model comparison is usually based on information criteria like the AIC, BIC or HQ. Usually, the AIC is preferred over other criteria, due to its favourable small sample forecasting features. The BIC and HQ, however, work well in large samples and have the advantage of being a consistent estimator of the true order, i.e. they prefer the true order of the VAR model - in contrast to the order, which yields the best forecasts - as the sample size grows.

The VAR function of the vars package already allows to calculate standard information criteria to find the best model. In this example we use the AIC:

Note that instead of specifying the order p, we now set the maximum lag length of the model and the information criterion used to select the best model. The function then estimates all five models, compares them according to their AIC values and automatically selects the most favourable. Looking at summary(var.aic) we see that the AIC suggests to use an order of 2 which is the true order.

Looking at the results more closely we can compare the true values - cointained in object A - with the parameter estimates of the model:

All the estimates have the right sign and are relatively close to their true values. I leave it to you to look at the standard errors of summary(var.aic) to check whether the true values fall into the confidence bands of the estimates.

Impulse response

Once we have decided on a final VAR model its estimated parameter values have to be interpreted. Since all variables in a VAR model depend on each other, individual parameter values only provide limited information on the reaction of the system to a shock. In order to get a better intuition of the model’s dynamic behaviour, impulse responses (IR) are used. They give the reaction of a response variable to a one-time shock in an impulse variable. The trajectory of the response variable can be plotted, which results in those wavy curves that can be found in many macro papers.

In R the irf function of the vars package can be used to obtain an impulse response function. In the following example, we want to know how Series 2 behaves after a shock to Series 1. After specifying the model and the variables for which we want an impulse response we set the time horizon n.ahead to 20. The plot gives the response of series 2 for the periods 0 to 20 to a shock in series 1 in period 0. The function also automatically calculates so-called bootstrap confidence bands. (Bootstrapping is a common procedure in impulse response analysis. But you should keep in mind that it has its drawbacks when you work with structural VAR models though.)

Note that the ortho option is important, because it says something about the contemporaneous relationships between the variables. In our example we already know that such relationships do not exist, because the true variance-covariance matrix – or simply covariance matrix – is diagonal with zeros in the off-diagonal elements. However, since the limited time series data with 200 observations restricts the precision of the parameter estimates, the covariance matrix has positive values in its off-diagonal elements which implies non-zero contemporaneous effects of a shock. To rule this out in the IR, we set ortho = FALSE. The result of this is that the impulse response starts at zero in period 0. You could also try out the alternative and set ortho = TRUE, which results in a plot that start below zero. I do not want to go into more detail here, but suffice it so say that the issue of so-called orthogonal errors is one of the central problems in VAR analysis and you should definitely read more about it, if you plan to set up your own VAR models.

Sometimes it is interesting to see what the long-run effects of a shock are. To get an idea about that you can also calculate and plot the cumulative impulse response function to get an idea of the overall long-run effect of the shock:

We see that although the reaction of series 2 to a shock in series 1 is negative during some periods, the overall effect significantly positive.

References

Lütkepohl, H. (2007). New Introduction to Multiple Time Series Analyis. Berlin: Springer.

Bernhard Pfaff (2008). VAR, SVAR and SVEC Models: Implementation Within R Package vars. Journal of Statistical Software 27(4).

Sims, C. (1980). Macroeconomics and Reality. Econometrica, 48(1), 1–48.

  1. If you want to impress your professor, you can also use the term Wold-ordering problem to refer to this issue.↩