# Parker-Hannifin Corporation (PH)

## Stock Price Trends

Stock price trends estimated using linear regression.

#### Key facts

• The primary trend is increasing.
• The growth rate of the primary trend is 43.81% per annum.
• PH price at the close of November 28, 2023 was \$426.53 and was inside the primary price channel.
• The secondary trend is increasing.
• The growth rate of the secondary trend is 3.13% per annum.
• PH price at the close of November 28, 2023 was inside the secondary price channel.

### 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 PH 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: June 10, 2022
End date: November 28, 2023

a = 4.2371

b = 0.0010

s = 0.0615

Annual growth rate:

Exp(365 × b) – 1
= Exp(365 × 0.0010) – 1
= 43.81%

Exp(4 × s) – 1
= Exp(4 × 0.0615) – 1
= 27.87%

#### June 10, 2022 calculations

Top border of price channel:

Exp(Y888)
= Exp(a + b × X888 + 2 × s)
= Exp(a + b × 1,289 + 2 × s)
= Exp(4.2371 + 0.0010 × 1,289 + 2 × 0.0615)
= Exp(5.6432)
= \$282.36

Bottom border of price channel:

Exp(Y888)
= Exp(a + b × X888 – 2 × s)
= Exp(a + b × 1,289 – 2 × s)
= Exp(4.2371 + 0.0010 × 1,289 – 2 × 0.0615)
= Exp(5.3973)
= \$220.81

#### November 28, 2023 calculations

Top border of price channel:

Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,825 + 2 × s)
= Exp(4.2371 + 0.0010 × 1,825 + 2 × 0.0615)
= Exp(6.1767)
= \$481.41

Bottom border of price channel:

Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(4.2371 + 0.0010 × 1,825 – 2 × 0.0615)
= Exp(5.9309)
= \$376.48

### Secondary Trend

Start date: June 29, 2023
End date: November 28, 2023

a = 5.8452

b = 0.0001

s = 0.0420

Annual growth rate:

Exp(365 × b) – 1
= Exp(365 × 0.0001) – 1
= 3.13%

Exp(4 × s) – 1
= Exp(4 × 0.0420) – 1
= 18.30%

#### June 29, 2023 calculations

Top border of price channel:

Exp(Y1,151)
= Exp(a + b × X1,151 + 2 × s)
= Exp(a + b × 1,673 + 2 × s)
= Exp(5.8452 + 0.0001 × 1,673 + 2 × 0.0420)
= Exp(6.0703)
= \$432.81

Bottom border of price channel:

Exp(Y1,151)
= Exp(a + b × X1,151 – 2 × s)
= Exp(a + b × 1,673 – 2 × s)
= Exp(5.8452 + 0.0001 × 1,673 – 2 × 0.0420)
= Exp(5.9023)
= \$365.86

#### November 28, 2023 calculations

Top border of price channel:

Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,825 + 2 × s)
= Exp(5.8452 + 0.0001 × 1,825 + 2 × 0.0420)
= Exp(6.0831)
= \$438.40

Bottom border of price channel:

Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(5.8452 + 0.0001 × 1,825 – 2 × 0.0420)
= Exp(5.9151)
= \$370.58