Paychex Inc (PAYX)
Paychex, Inc. is a leading provider of comprehensive human resource, payroll, and benefits outsourcing solutions tailored specifically for small- and medium-sized businesses. Headquartered in Rochester, New York, the company leverages advanced technology and a client-centric approach to streamline workforce management processes for its clients. Committed to delivering value and efficiency, Paychex offers a robust suite of services, including payroll processing, tax administration, and employee benefit management. With a strong reputation for reliability and customer service, Paychex continues to expand its footprint in the HR services market, making it a key player in supporting the growth and success of its clients.
Stock Price Trends
Stock price trends estimated using linear regression.
Key facts
- The primary trend is decreasing.
- The decline rate of the primary trend is 45.45% per annum.
- PAYX price at the close of December 24, 2025 was $114.58 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 64.06% per annum.
- PAYX price at the close of December 24, 2025 was inside the secondary price channel.
- The direction of the secondary trend is opposite to the direction of the primary trend. This indicates a possible reversal in the direction of the primary trend.
Linear Regression Model
Model equation:
Yi = α + β × Xi + εi
Top border of price channel:
Exp(Yi) = Exp(a + b × Xi + 2 × s)
Bottom border of price channel:
Exp(Yi) = Exp(a + b × Xi – 2 × s)
where:
i - observation number
Yi - natural logarithm of PAYX price
Xi - time index, 1 day interval
σ - standard deviation of εi
a - estimator of α
b - estimator of β
s - estimator of σ
Exp() - calculates the exponent of e
Primary Trend
Start date: May 15, 2025
End date: December 23, 2025
a = 7.7197
b = -0.0017
s = 0.0277
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0017) – 1
= -45.45%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0277) – 1
= 11.73%
May 15, 2025 calculations
Top border of price channel:
Exp(Y1,100)
= Exp(a + b × X1,100 + 2 × s)
= Exp(a + b × 1,599 + 2 × s)
= Exp(7.7197 + -0.0017 × 1,599 + 2 × 0.0277)
= Exp(5.1198)
= $167.31
Bottom border of price channel:
Exp(Y1,100)
= Exp(a + b × X1,100 – 2 × s)
= Exp(a + b × 1,599 – 2 × s)
= Exp(7.7197 + -0.0017 × 1,599 – 2 × 0.0277)
= Exp(5.0089)
= $149.74
December 23, 2025 calculations
Top border of price channel:
Exp(Y1,253)
= Exp(a + b × X1,253 + 2 × s)
= Exp(a + b × 1,821 + 2 × s)
= Exp(7.7197 + -0.0017 × 1,821 + 2 × 0.0277)
= Exp(4.7512)
= $115.72
Bottom border of price channel:
Exp(Y1,253)
= Exp(a + b × X1,253 – 2 × s)
= Exp(a + b × 1,821 – 2 × s)
= Exp(7.7197 + -0.0017 × 1,821 – 2 × 0.0277)
= Exp(4.6403)
= $103.57
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 45.45% per annum.
- PAYX price at the close of December 24, 2025 was $114.58 and was inside the primary price channel.
Secondary Trend
Start date: November 17, 2025
End date: December 24, 2025
a = 2.2771
b = 0.0014
s = 0.0104
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0014) – 1
= 64.06%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0104) – 1
= 4.24%
November 17, 2025 calculations
Top border of price channel:
Exp(Y1,228)
= Exp(a + b × X1,228 + 2 × s)
= Exp(a + b × 1,785 + 2 × s)
= Exp(2.2771 + 0.0014 × 1,785 + 2 × 0.0104)
= Exp(4.7191)
= $112.06
Bottom border of price channel:
Exp(Y1,228)
= Exp(a + b × X1,228 – 2 × s)
= Exp(a + b × 1,785 – 2 × s)
= Exp(2.2771 + 0.0014 × 1,785 – 2 × 0.0104)
= Exp(4.6775)
= $107.50
December 24, 2025 calculations
Top border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 + 2 × s)
= Exp(a + b × 1,822 + 2 × s)
= Exp(2.2771 + 0.0014 × 1,822 + 2 × 0.0104)
= Exp(4.7693)
= $117.83
Bottom border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 – 2 × s)
= Exp(a + b × 1,822 – 2 × s)
= Exp(2.2771 + 0.0014 × 1,822 – 2 × 0.0104)
= Exp(4.7277)
= $113.03
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 64.06% per annum.
- PAYX price at the close of December 24, 2025 was inside the secondary price channel.