# Pitney Bowes Inc (PBI)

Pitney Bowes Inc., a technology company, offers business solutions in the United States and internationally. The company is headquartered in Stamford, Connecticut.

## 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 69.31% per annum.
• PBI price at the close of August 12, 2024 was \$6.92 and was higher than the top border of the primary price channel by \$0.00 (0.01%).
• The secondary trend is increasing.
• The growth rate of the secondary trend is 243.41% per annum.
• PBI price at the close of August 12, 2024 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 PBI 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 1, 2023
End date: August 12, 2024

a = -0.9117

b = 0.0014

s = 0.1059

Annual growth rate:

Exp(365 × b) – 1
= Exp(365 × 0.0014) – 1
= 69.31%

Exp(4 × s) – 1
= Exp(4 × 0.1059) – 1
= 52.72%

#### May 1, 2023 calculations

Top border of price channel:

Exp(Y935)
= Exp(a + b × X935 + 2 × s)
= Exp(a + b × 1,357 + 2 × s)
= Exp(-0.9117 + 0.0014 × 1,357 + 2 × 0.1059)
= Exp(1.2577)
= \$3.52

Bottom border of price channel:

Exp(Y935)
= Exp(a + b × X935 – 2 × s)
= Exp(a + b × 1,357 – 2 × s)
= Exp(-0.9117 + 0.0014 × 1,357 – 2 × 0.1059)
= Exp(0.8343)
= \$2.30

#### August 12, 2024 calculations

Top border of price channel:

Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(-0.9117 + 0.0014 × 1,826 + 2 × 0.1059)
= Exp(1.9343)
= \$6.92

Bottom border of price channel:

Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(-0.9117 + 0.0014 × 1,826 – 2 × 0.1059)
= Exp(1.5109)
= \$4.53

#### Description

• The primary trend is increasing.
• The growth rate of the primary trend is 69.31% per annum.
• PBI price at the close of August 12, 2024 was \$6.92 and was higher than the top border of the primary price channel by \$0.00 (0.01%).

### Secondary Trend

Start date: February 20, 2024
End date: August 12, 2024

a = -4.2817

b = 0.0034

s = 0.0822

Annual growth rate:

Exp(365 × b) – 1
= Exp(365 × 0.0034) – 1
= 243.41%

Exp(4 × s) – 1
= Exp(4 × 0.0822) – 1
= 38.95%

#### February 20, 2024 calculations

Top border of price channel:

Exp(Y1,137)
= Exp(a + b × X1,137 + 2 × s)
= Exp(a + b × 1,652 + 2 × s)
= Exp(-4.2817 + 0.0034 × 1,652 + 2 × 0.0822)
= Exp(1.4668)
= \$4.34

Bottom border of price channel:

Exp(Y1,137)
= Exp(a + b × X1,137 – 2 × s)
= Exp(a + b × 1,652 – 2 × s)
= Exp(-4.2817 + 0.0034 × 1,652 – 2 × 0.0822)
= Exp(1.1378)
= \$3.12

#### August 12, 2024 calculations

Top border of price channel:

Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(-4.2817 + 0.0034 × 1,826 + 2 × 0.0822)
= Exp(2.0550)
= \$7.81

Bottom border of price channel:

Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(-4.2817 + 0.0034 × 1,826 – 2 × 0.0822)
= Exp(1.7260)
= \$5.62

#### Description

• The secondary trend is increasing.
• The growth rate of the secondary trend is 243.41% per annum.
• PBI price at the close of August 12, 2024 was inside the secondary price channel.