# 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:

Y_{i} = α + β × X_{i} + ε_{i}

Top border of price channel:

Exp(Y_{i}) = Exp(a + b × X_{i} + 2 × s)

Bottom border of price channel:

Exp(Y_{i}) = Exp(a + b × X_{i} – 2 × s)

where:

i - observation number

Y_{i} - natural logarithm of PBI price

X_{i} - time index, 1 day interval

σ - standard deviation of ε_{i}

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%

Price channel spread:

Exp(4 × s) – 1

= Exp(4 × 0.1059) – 1

= 52.72%

#### May 1, 2023 calculations

Top border of price channel:

Exp(Y_{935})

= Exp(a + b × X_{935} + 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(Y_{935})

= Exp(a + b × X_{935} – 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(Y_{1,257})

= Exp(a + b × X_{1,257} + 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(Y_{1,257})

= Exp(a + b × X_{1,257} – 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%

Price channel spread:

Exp(4 × s) – 1

= Exp(4 × 0.0822) – 1

= 38.95%

#### February 20, 2024 calculations

Top border of price channel:

Exp(Y_{1,137})

= Exp(a + b × X_{1,137} + 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(Y_{1,137})

= Exp(a + b × X_{1,137} – 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(Y_{1,257})

= Exp(a + b × X_{1,257} + 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(Y_{1,257})

= Exp(a + b × X_{1,257} – 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.