
602 F.3d 374 (2010)
L. Wayne JACKSON, Plaintiff-Appellant,
v.
CAL-WESTERN PACKAGING CORPORATION, Defendant-Appellee.
No. 09-20411.
United States Court of Appeals, Fifth Circuit.
March 26, 2010.
*376 Otto D. Hewitt, III, Hewitt Law Firm, Alvin, TX, for Jackson.
Maryanne Lyons, Jarod Douglas Bonine, Baker Botts, L.L.P., Houston, TX, Kris Holub Tilley, Jo Ellen Whitney, Davis, Brown, Koehn, Shors & Roberts, P.C., Des Moines, IA, for Defendant-Appellee.
Before SMITH, CLEMENT and OWEN, Circuit Judges.
OWEN, Circuit Judge:
Wayne Jackson brought claims under the Age Discrimination in Employment Act (ADEA), 29 U.S.C. §§ 621-634, and appeals the district court's grant of summary judgment in favor of his employer. We affirm.

I
Jackson was employed by Cal-Western Packaging Corporation in various managerial positions for eight years, until June 2007. In May 2007, one of Jackson's coworkers, Karen Hopper, emailed her supervisor, Cal-Western Controller James Rosetti, asserting that Jackson had engaged in behavior that made her "uncomfortable." She recounted that Jackson had asked to see her "[breasts]" and had commented that her boyfriend must like "big boobs." She stated that Jackson had "on many occasions" made inappropriate statements or comments in front of her and her female coworkers. In addition, she told her supervisor that every time she saw Jackson he tried to touch her and that he had once cornered her and asked her to raise her blouse. Rosetti then informed Chief Operating Officer Jimmy Phelps of Jackson's behavior. Phelps began an internal investigation and interviewed several employees who corroborated the allegations. Phelps then hired an attorney, Victoria Phipps, to conduct an external investigation into Jackson's behavior. Phipps's interviews with both male and female coworkers confirmed the harassment allegations. When Phipps interviewed Jackson, he asserted that he was "vindictive" and would try "legally" to retaliate against those making allegations against him.
In June 2007, Phelps terminated Jackson for his non-compliance with the company's written sexual harassment policy, a copy of which Jackson had signed when he was hired in 1999. Jackson was sixty-nine years old when he was terminated. He was replaced by Monte Duke, who was forty-two at the time.
Jackson brought suit against Cal-Western for age discrimination. His claim primarily relied on a remark Phelps allegedly made to another coworker in 2006 to the effect that Jackson was an "old, gray-haired fart" and that the coworker would be in charge when Jackson retired. Cal-Western moved for summary judgment. The district court ruled that Jackson had alleged a prima facie case of discrimination and that Cal-Western had offered a legitimate, non-discriminatory reason for firing him, but that Jackson had failed to show that there was a fact issue as to whether Cal-Western's reason for firing him was pretextual. Jackson argues on appeal that the district court decided factual issues at the summary judgment stage and improperly relied on incompetent summary judgment evidence in its ruling.


*377 II
Jackson first challenges the district court's reliance on several sworn, notarized affidavits tendered by Cal-Western as summary judgment evidence. Jackson argues that the affidavits are not competent summary judgment evidence since they do not state that they were sworn to be "true and correct."
Jackson's argument is without merit. The cases on which he relies all relate to unsworn affidavits. None of the statements at issue in this case were unsworn. Additionally, we have expressly held that "there is no requirement that sworn affidavits have a statement that the contents are `true and correct.'"[1] "Sworn affidavits ... are certainly appropriate for review on a Rule 56 motion for summary judgment."[2] Accordingly, the district court properly relied on the sworn affidavits.

III
We review the grant of a motion for summary judgment de novo, applying the same standard as the district court.[3] We view the evidence in the light most favorable to the non-moving party and avoid credibility determinations and weighing of the evidence.[4] Summary judgment is appropriate when the competent summary judgment evidence demonstrates that there are no genuine issues of material fact and the moving party is entitled to judgment as a matter of law.[5] An issue of material fact is genuine if a reasonable jury could return a verdict for the nonmovant.[6]
In employment discrimination cases, a plaintiff may rely on direct or circumstantial evidence, or both.[7] Under the ADEA, the plaintiff has the burden of persuasion to show "that age was the `butfor' cause of [his] employer's adverse action."[8]
Jackson first argues that Phelps's purported comment that he was an "old, gray-haired fart" is direct evidence of age discrimination. But since Jackson did not make this argument in his response to the summary judgment motion before the district court, he is precluded from raising it on appeal.[9] Moreover, the comment is not direct evidence of discrimination. As we will discuss further infra, Jackson has not shown that the comment was proximate in time to the termination or related to the employment decision, and thus the comment cannot qualify as direct evidence.[10]
Jackson contended in the district court and maintains on appeal that circumstantial evidence establishes his claim of age discrimination. The district court applied *378 the familiar framework outlined in McDonnell Douglas Corp. v. Green[11] for allocating the burden of production and the order of presenting proof.[12] "Although intermediate evidentiary burdens shift back and forth under this framework, `[t]he ultimate burden of persuading the trier of fact that the defendant intentionally discriminated against the plaintiff remains at all times with the plaintiff.'"[13]
Neither party has contended on appeal that the McDonnell Douglas framework is inapplicable to ADEA claims. While the Supreme Court has not definitively resolved whether it is,[14] we are bound by our circuit precedent applying McDonnell Douglas to age discrimination cases.[15] Accordingly, we will consider Jackson's claims involving circumstantial evidence under that construct.
To establish a prima facie case of age discrimination, "a plaintiff must show that (1) he was discharged; (2) he was qualified for the position; (3) he was within the protected class at the time of discharge; and (4) he was either i) replaced by someone outside the protected class, ii) replaced by someone younger, or iii) otherwise discharged because of his age."[16] The parties do not dispute that Jackson has alleged a prima facie case of age discrimination since he was terminated, qualified, forty years or older (and thus within the class protected by the ADEA),[17] and replaced by someone substantially younger.[18]
Nor do the parties dispute that Cal-Western has articulated a legitimate, non-discriminatory reason for Jackson's termination with its explanation that he was fired for sexual harassment. The question is whether Jackson has shown that there is a genuine issue of material fact as to whether this reason was pretextual. A plaintiff may show pretext "either through evidence of disparate treatment or *379 by showing that the employer's proffered explanation is false or `unworthy of credence.'"[19]
Jackson asserts that the evidence in the record creates a factual issue as to whether Cal-Western's proffered reason was pretextual. Specifically, he points to: (1) his own statements that he had not made sexually harassing comments; (2) Phelps's purported statement that he was an "old, gray-haired fart;" (3) evidence that Cal-Western did not discipline younger employees who engaged in similar commentary and emails; and (4) a coworker's statement that she did not perceive his alleged comments as sexual harassment.
Jackson's self-serving statements that he did not commit sexual harassment are insufficient to create a triable issue of fact as to whether Cal-Western fired him because of his age. In cases in which an employer discharges an employee based on the complaint of another employee, the issue is not the truth or falsity of the allegation, but "whether the employer reasonably believed the employee's allegation and acted on it in good faith."[20] Cal-Western was faced with considerable evidence that Jackson was violating the company's sexual harassment policy. The evidence came from several employees, both male and female, and was substantiated by both an internal and external investigation of Jackson's behavior. Jackson has presented no evidence as to why the company's reliance on the evidence against him was in bad faith. His own conclusory assertion that he did not behave inappropriately is irrelevant, since he has provided no evidence to suggest that Cal-Western's decision to trust the results of the two investigations, rather than his self-serving denial of wrongdoing, was unreasonable or in bad faith.[21] Jackson's assertion of innocence alone does not create a factual issue as to the falsity of Cal-Western's proffered reason for terminating him.[22]
Jackson's assertions that Cal-Western did not discipline younger employees who engaged in similar behavior and that Jackson's coworker stated that his behavior did not amount to sexual harassment cannot be used to establish triable issues of fact since he did not make these assertions in the district court or refer to any evidence to this effect.[23] (Nor does he refer to any evidence of this nature in his brief to this court.) We have explained that "Rule 56 does not impose upon the district court a duty to sift through the record in search of evidence to *380 support a party's opposition to summary judgment."[24] Because Jackson did not identify any such evidence in his opposition to summary judgment, we will not consider his argument in this regard.
Finally, we turn to Phelps's alleged comment. In his deposition, Jackson stated that coworker Donnie Sheets "told me one day in his office that [Phelps] had told him that he was going to be in charge of all the plants when that old, gray-haired fart retired, meaning me."[25] Jackson said that Sheets made this comment to him "a couple of times," but he did not discuss whether Phelps made the comment to Sheets on more than one occasion. The district court concluded that Phelps's statement was a "stray remark."
We have explained that comments are evidence of discrimination only if they are "1) related to the protected class of persons of which the plaintiff is a member; 2) proximate in time to the complained-of adverse employment decision; 3) made by an individual with authority over the employment decision at issue; and 4) related to the employment decision at issue."[26] Comments that do not meet these criteria are considered "stray remarks,"[27] and standing alone, are insufficient to defeat summary judgment.[28]
While Phelps's alleged comment meets the first and third criteria, Jackson has provided no evidence that the comment was proximate in time to his firing or related to the employment decision at issue. Jackson maintains that Sheets told him of Phelps's comment on a visit to Memphis in the summer of 2006, but it is unclear when Phelps actually made the comment. Still, even assuming that the comment was made soon before Sheets reported it to Jackson, it was made almost a year before Jackson's June 2007 termination. The comment appears wholly unrelated to Jackson's termination, and Jackson has not presented any evidence to show otherwise.
This comment alone, or in combination with Jackson's uncorroborated denial of any sexual harassment, is insufficient to establish a genuine issue of material fact as to pretext.[29] There is substantial evidence *381 that Jackson was fired for violation of Cal-Western's sexual harassment policy, and Jackson's only contravention of that evidence comes from his own assertions. Without more, we simply cannot conclude that there is a triable issue of fact as to whether Cal-Western discriminated against Jackson based on age.

* * *
Because no genuine issue of material fact exists as to Jackson's claim under the ADEA, we AFFIRM the district court's grant of summary judgment for Cal-Western.
NOTES
[1]  DIRECTV, Inc. v. Budden, 420 F.3d 521, 530 (5th Cir.2005).
[2]  E.E.O.C. v. WC&M Enters., Inc., 496 F.3d 393, 398 (5th Cir.2007).
[3]  Threadgill v. Prudential Sec. Group, Inc., 145 F.3d 286, 292 (5th Cir. 1998).
[4]  Sandstad v. CB Richard Ellis, Inc., 309 F.3d 893, 896 (5th Cir.2002).
[5]  Brumfield v. Hollins, 551 F.3d 322, 326 (5th Cir.2008).
[6]  Anderson v. Liberty Lobby, Inc., 477 U.S. 242, 248, 106 S.Ct. 2505, 91 L.Ed.2d 202 (1986).
[7]  Sandstad, 309 F.3d at 896.
[8]  Gross v. FBL Fin. Servs., Inc., ___ U.S. ___, 129 S.Ct. 2343, 2351, 174 L.Ed.2d 119 (2009).
[9]  See Vogel v. Veneman, 276 F.3d 729, 733 (5th Cir.2002).
[10]  See Palasota v. Haggar Clothing Co., 342 F.3d 569, 576 (5th Cir.2003).
[11]  411 U.S. 792, 93 S.Ct. 1817, 36 L.Ed.2d 668 (1973).
[12]  See Reeves v. Sanderson Plumbing Prods., Inc., 530 U.S. 133, 142-43, 120 S.Ct. 2097, 147 L.Ed.2d 105 (2000) (explaining that "[f]irst, the plaintiff must establish a prima facie case of discrimination," which shifts to respondent the burden to "produc[e] evidence that the plaintiff was rejected, or someone else was preferred, for a legitimate, nondiscriminatory reason .... This burden is one of production, not persuasion; it `can involve no credibility assessment.'" If this burden is met, the plaintiff "must be afforded the `opportunity to prove by a preponderance of the evidence that the legitimate reasons offered by the defendant were not its true reasons, but were a pretext for discrimination.'" (internal citations omitted)).
[13]  Id. at 143, 120 S.Ct. 2097 (quoting Tex. Dep't of Cmty. Affairs v. Burdine, 450 U.S. 248, 253, 101 S.Ct. 1089, 67 L.Ed.2d 207 (1981)).
[14]  See Gross v. FBL Fin. Servs., Inc., ___ U.S. ___, 129 S.Ct. 2343, 2349 n. 2, 174 L.Ed.2d 119 (2009) ("[T]he Court has not definitively decided whether the evidentiary framework of [McDonnell Douglas], utilized in Title VII cases is appropriate in the ADEA context.").
[15]  See Baker v. Am. Airlines, Inc., 430 F.3d 750, 753 (5th Cir.2005); Machinchick v. PB Power, Inc., 398 F.3d 345, 350 (5th Cir.2005); Patrick v. Ridge, 394 F.3d 311, 315 (5th Cir. 2004); Sandstad v. CB Richard Ellis, Inc., 309 F.3d 893, 896-97 (5th Cir.2002); Bodenheimer v. PPG Indus., Inc., 5 F.3d 955, 957 (5th Cir.1993).
[16]  Berquist v. Wash. Mut. Bank, 500 F.3d 344, 349 (5th Cir.2007) (internal quotation marks and citation omitted).
[17]  See 29 U.S.C. § 631(a) (protecting individuals "who are at least 40 years of age").
[18]  See O'Connor v. Consol. Coin Caterers Corp., 517 U.S. 308, 312-13, 116 S.Ct. 1307, 134 L.Ed.2d 433 (1996) (explaining that replacement by someone "substantially younger" can be an indicator of age discrimination).
[19]  Laxton v. Gap Inc., 333 F.3d 572, 578 (5th Cir.2003) (quoting Reeves, 530 U.S. at 143, 120 S.Ct. 2097).
[20]  Waggoner v. City of Garland, 987 F.2d 1160, 1165 (5th Cir. 1993).
[21]  See id. at 1166 (explaining that, since bad faith is the issue, "[t]o the extent that Waggoner's summary judgment evidence relates to his innocence of the sexual harassment charge, it is irrelevant").
[22]  Cf. Vais Arms, Inc. v. Vais, 383 F.3d 287, 294 (5th Cir.2004) (concluding that self-serving statements were insufficient to overcome summary judgment, particularly when faced with "overwhelming evidence" in opposition); United States v. Lawrence, 276 F.3d 193, 197 (5th Cir.2001) (affirming summary judgment for the plaintiff when defendant's only evidence in opposition was his own "self-serving allegations"); BMG Music v. Martinez, 74 F.3d 87, 91 (5th Cir.1996) (explaining that a "conclusory, self-serving statement" by defendant was insufficient to create a triable issue of fact).
[23]  See Malacara v. Garber, 353 F.3d 393, 405 (5th Cir.2003) (stating that "[w]hen evidence exists in the summary judgment record but the nonmovant fails even to refer to it in the response to the motion for summary judgment, that evidence is not properly before the district court").
[24]  Id. (quoting Ragas v. Tenn. Gas Pipeline Co., 136 F.3d 455, 458 (5th Cir.1998)).
[25]  Phelps and Sheets have both denied that Phelps made such a comment, but since we do not make credibility determinations at the summary judgment stage, their denials are irrelevant.
[26]  Rubinstein v. Adm'rs of Tulane Educ. Fund, 218 F.3d 392, 400-01 (5th Cir.2000) (internal brackets and quotation marks omitted).
[27]  We have explained that this circuit's stray remarks doctrine survived the Supreme Court's decision in Reeves v. Sanderson Plumbing Products, Inc., 530 U.S. 133, 120 S.Ct. 2097, 147 L.Ed.2d 105 (2000). See Auguster v. Vermilion Parish Sch. Bd., 249 F.3d 400, 405 (5th Cir.2001) (noting that a post-Reeves decision by which we are bound, Rubinstein, 218 F.3d 392 (5th Cir.2000), interpreted Reeves not to overrule the stray remarks doctrine); cf. Russell v. McKinney Hosp. Venture, 235 F.3d 219, 229 (5th Cir. 2000) (explaining that we should view the stray remarks doctrine "cautiously" after Reeves).
[28]  Rubinstein, 218 F.3d at 401; see also Waggoner v. City of Garland, 987 F.2d 1160, 1166 (5th Cir.1993) ("[A] mere `stray remark' is insufficient to establish age discrimination.").
[29]  See Auguster, 249 F.3d at 405 (holding that a comment made nearly a year before the adverse employment decision that appeared unrelated to the decision was a stray remark); see also Patel v. Midland Mem'l Hosp. & Med. Ctr., 298 F.3d 333, 344 (5th Cir.2002) (holding that a comment made two or more years before the employment decision at issue, that was unrelated to the decision, was not evidence of discrimination); Wallace v. Methodist Hosp. Sys., 271 F.3d 212, 222 (5th Cir. 2001) (stating that "where comments are vague and remote in time they are insufficient to establish discrimination" (internal brackets and quotation marks omitted)); Rubinstein, 218 F.3d at 401 (concluding that comments were stray remarks when plaintiff had failed to offer evidence that they were proximate in time or related to his failure to receive a raise or a promotion).
