<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2019-01-15</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001008848</issuerCik>
        <issuerName>ACORDA THERAPEUTICS INC</issuerName>
        <issuerTradingSymbol>ACOR</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001279150</rptOwnerCik>
            <rptOwnerName>SCOPIA CAPITAL MANAGEMENT LP</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>152 WEST 57TH STREET, 33RD FLOOR</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10019</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001665995</rptOwnerCik>
            <rptOwnerName>Scopia Management, Inc.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>152 WEST 57TH STREET, 33RD FLOOR</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10019</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001431208</rptOwnerCik>
            <rptOwnerName>SIROVICH MATTHEW</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>152 WEST 57TH STREET, 33RD FLOOR</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10019</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001431207</rptOwnerCik>
            <rptOwnerName>MINDICH JEREMY</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>152 WEST 57TH STREET, 33RD FLOOR</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10019</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2019-01-15</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1700</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>16.6018</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>5097071</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2019-01-16</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>91650</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>16.9385</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>5005421</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">This Form 4 is filed jointly by Scopia Capital Management LP (&quot;Scopia Management&quot;), Scopia Management, Inc. (&quot;Scopia Inc.&quot;), Matthew Sirovich and Jeremy Mindich. The securities reported in this Form 4 are held in the accounts of several private investment funds, including Scopia Long LLC, Scopia Windmill Fund LP, Scopia International Master Fund LP, Scopia PX LLC, Scopia PX International Master Fund LP, Scopia Partners LLC, Scopia Long International Master Fund LP, Scopia Long QP LLC, Scopia Health Care LLC, Scopia Health Care International Master Fund LP and Scopia LB LLC (together, the &quot;Investment Vehicles&quot;) for which Scopia Management serves as the investment manager. Each of the Investment Vehicles individually holds less than 10% of the outstanding shares of common stock of Acorda Therapeutics, Inc. (the &quot;Issuer&quot;). Scopia Management, as the investment manager of the Investment Vehicles,</footnote>
        <footnote id="F2">(Continued from footnote 1) may be deemed to indirectly beneficially own the shares of common stock of the Issuer held directly by the Investment Vehicles because Scopia Management has voting and investment power over such securities. In addition, Scopia Inc., as general partner of Scopia Management, and Matthew Sirovich and Jeremy Mindich, as Managing Directors of Scopia Inc., may be deemed to indirectly beneficially own the shares of common stock of the Issuer held directly by the Investment Vehicles because each of Scopia Inc., Mr. Sirovich and Mr. Mindich may be deemed to exercise voting and investment power over such securities.  Further, Messrs. Sirovich and Mindich may be deemed to have a pecuniary interest in a portion of the securities held directly by the Investment Vehicles due to the right of an affiliate of Scopia Management to receive performance-based allocations and due to their investments in the Investment Vehicles.</footnote>
        <footnote id="F3">Each of Scopia Management, Scopia Inc. and Messrs. Sirovich and Mindich disclaims beneficial ownership of the securities reported herein except to the extent of his or its pecuniary interest therein, and this report shall not be deemed an admission that any of Scopia Management, Scopia Inc. or Messrs. Sirovich and Mindich is the beneficial owner of such securities for purposes of Section 16 of the Securities Exchange Act of 1934, as amended, or for any other purpose.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>SCOPIA CAPITAL MANAGEMENT LP, By: Scopia Management, Inc., its general partner, Name: /s/ Matthew Sirovich, Title: Managing Director</signatureName>
        <signatureDate>2019-01-17</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>SCOPIA MANAGEMENT, INC., Name: /s/ Matthew Sirovich, Title: Managing Director</signatureName>
        <signatureDate>2019-01-17</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Matthew Sirovich</signatureName>
        <signatureDate>2019-01-17</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Jeremy Mindich</signatureName>
        <signatureDate>2019-01-17</signatureDate>
    </ownerSignature>
</ownershipDocument>
